PRACTICAL  PHYSICS 


MILLIKAN  AND  GALE 


GIFT   OF 
Agriculture  education 


PEACTICAL  PHYSICS 


BY 

EGBERT  ANDREWS  MILLIKAN,  PH.D.,  Sc.D. 

DIRECTOR  OF  THE  NORMAN  BRIDGE   LABORATORY  OF 
PHYSICS,  PASADENA,  CALIFORNIA 

AND 

HENRY  GORDON  GALE,  PH.D. 

PROFESSOR  OF   PHYSICS  IN  THE   UNIVERSITY    OF   CHICAGO 


BEING  A  REVISION  OF  THE  AUTHORS'  "A  FIRST  COURSE  IN 
PHYSICS"  DONE  IN  COLLABORATION  WITH 

WILLARD  R.  PYLE,  B.S. 

HEAD  OF  THE  DEPARTMENT   OF  PHYSICS,  MORRIS  HIGH  SCHOOL 
NEW  YORK  CITY 


GTNN  AND  COMPANY 

BOSTON     •     NEW  YORK     •     CHICAGO     •     LONDON 
ATLANTA     •    DALLAS     •     COLUMBUS     •     SAN  FRANCISCO 


COPYRIGHT,  1906,  1913,  BY  ROBERT  A.  MILLIKAN 
AND  HENRY  G.  GALE 


COPYRIGHT,  1920,  1922,   BY  GINN  AND  COMPANY 

ENTERED   AT   STATIONERS'   HALL 

ALL  RIGHTS   RESERVED 

B424.1  tflfb 


A6RIO,  OFPT. 


, 


GINN  AND  COMPANY  •  PRO 
PRIETORS  •  BOSTON  •  U.S.A. 


PREFACE 

The  chief  aim  of  this  book  in  all  of  its  editions  has  been  to 
present  elementary  physics  in  such  a  way  as  to  stimulate  the 
pupil  to  do  some  thinking  on  his  own  account  about  the  hows 
and  whys  of  the  physical  world  in  which  he  lives.  To  this  end 
such  subjects,  and  only  such  subjects,  have  been  included  as 
touch  most  closely  the  everyday  life  of  the  average  pupil.  In 
a  word,  the  endeavor  has  been  to  make  this  book  represent 
the  practical,  everyday  physics  which  the  average  person 
needs  to  help  him  to  adjust  himself  to  his  surroundings  and 
to  interpret  his  own  experiences  correctly. 

But  the  conditions  of  modern  life  are  changing  at  an  aston- 
ishing rate  and  calling  for  the  continuous  revision  of  any  text 
which  would  keep  pace  with  them.  For  example,  within  the 
past  ten  years  the  internal-combustion  engine  has  not  only 
taken  its  place  as  an  agent  of  equal  importance  with  the 
steam  engine  in  the  world's  industries  but,  what  is  more  im- 
portant, it  has  also  come  more  fully  into  the  daily  life  of  the 
average  man  and  woman  than  even  the  dynamo  and  motor 
have  ever  begun  to  do.  The  automobile  is  accordingly  given 
fuller  treatment  in  this  new  book  than  it  has  ever  received 
before  in  any  elementary  physics  text. 

Again,  man's  conquest  of  the  air,  after  centuries  of  failure, 
is  not  only  the  most  significant  advance,  on  the  practical  side, 
of  the  twentieth  century,  but  the  airplane  now  attracts  the 
attention  and  excites  the  interest  of  almost  every  man, 
woman,  and  child.  Accordingly,  the  principles  underlying 
this  advance,  and  the  methods  by  which  it  was  brought 
about,,  find  as  full  treatment  in  this  volume  as  is  consistent 

iii 

55752S 


iv  PKEFACE 

with  the  simplicity  and  clearness  demanded  in  a  beginning 
course  in  physics.  The  book  may  be  used,  if  desired,  even 
in  the  second  year  of  the  high  school. 

Further,  the  World  War  was  responsible  not  only  for 
extraordinary  developments  in  physics  but  also  for  demon- 
strating, both  to  the  American  youth  and  to  the  leader  of 
American  industry,  the  necessity  of  the  more  intensive  cul- 
tivation of  physical  science.  These  developments  and  these 
new  demands,  with  which  the  authors  came  into  the  closest 
touch  because  of  their  service  in  the  army  both  in  this 
country  and  in  France,  have  been  fully  reflected  in  this 
book,  the  emphasis,  however,  being  placed  upon  develop- 
ments which  make  for  peace  rather  than  for  war. 

As  in  preceding  editions,  the  full-page  inserts,  though  a  very 
vital  part  of  the  book,  are  not  a  necessary  and  integral  part 
of  the  course.  They  have  been  inserted,  in  more  than  double 
their  former  number,  in  order  to  add  human  and  historic  in- 
terest and  to  stimulate  the  pupil  to  look  farther  into  a  sub- 
ject than  his  immediate  assignment  requires  him  to  do.  It  is 
thought  that  they  will  be  found  to  be  an  invaluable  adjunct 
to  the  course. 

Both  the  order  and  the  treatment  are  in  many  places 
markedly  different  from  those  of  preceding  editions,  and 
reflect  the  experience  of  the  tens  of  thousands  of  teachers 
who  have  used  this  course,  many  of  whom  have  assisted  the 
authors  with  their  suggestions.  Especially  in  the  problems 
have  important  improvements  been  made. 

For  the  sake  of  indicating  in  what  directions  omissions 
may  be  made,  if  necessary,  without  interfering  with  con- 
tinuity, paragraphs  have  here  and  there,  as  in  former  editions, 
been  thrown  into  fine  print.  These  paragraphs  will  be  easily 
distinguished  from  the  classroom  experiments,  which  are  in 
the  same  type.  They  are  for  the  most  part  descriptions  of 
physical  appliances. 


PREFACE  v 

The  authors  are  under  great  obligation  to  all  of  their 
friends  who  have  assisted  them  in  this  work,  particularly  to 
their  collaborator,  Mr.  W.  R.  Pyle ;  also  to  Mr.  J.  R.  Towne 
of  East  High  School,  Minneapolis,  Mr.  C.  F.  Button,  of  the 
West  High  School  of  Commerce,  Cleveland,  Mr.  E.  Waite 
Elder,  of  the  Eastside  High  School,  Denver,  Mr.  C.  E.  Harris, 
of  the  East  High  School,  Rochester,  N.  Y.,  Mr.  Walter  L. 
Barnum  and  Mr.  Robert  E.  Hughes,  of  the  Evanston  High 
School,  Evanston,  111.,  and  Dr.  George  de  Bothezat,  aeronaut- 
ical expert  of  the  Advisory  Commission  for  Aeronautics. 

R.  A.  MILLIKAN 
H.  G.  GALE 


CONTENTS 

CHAPTER  PAGE 

I.  MEASUREMENT 1 

Fundamental  Units.   Density 
II.  PRESSURE  IN  LIQUIDS 11 

Liquid  Pressure  beneath  a  Free  Surface.  Pascal's  Law.  The 
Principle  of  Archimedes 

III.  PRESSURE  IN  AIR 26 

Barometric  Phenomena.  Compressibility  and  Expansibility 
of  Air.  Pneumatic  Appliances 

IV.  MOLECULAR  MOTIONS 49 

Kinetic  Theory  of  Gases.  Molecular  Motions  in  Liquids. 
Molecular  Motions  in  Solids 

V.  FORCE  AND  MOTION 57 

Definition  and  Measurement  of  Force.  Composition  and  Reso- 
lution of  Forces.  Gravitation.  Falling  Bodies.  Newton's  Laws 

VI.  MOLECULAR  FORCES 90 

Elasticity.    Capillary  Phenomena.   Absorption  of  Gases 
VII.  WORK  AND  MECHANICAL  ENERGY 105 

Definition  and  Measurement  of  Work.  Work  and  the  Pulley. 
Work  and  the  Lever.  The  Principle  of  Work.  Power  and 
Energy 

VIII.  THERMOMETRY  ;  EXPANSION  COEFFICIENTS     ....    128 
Thermometry.     Expansion  Coefficient  of  Gases.    Expansion    • 
of  Liquids  and  Solids.   Applications  of  Expansion 

IX.  WORK  AND  HEAT  ENERGY 144 

Friction.  Efficiency.  Mechanical  Equivalent  of  Heat.  Specific 
Heat 

X.  CHANGE  OF  STATE 161 

Fusion.  Properties  of  Vapors.   Hygrometry.  Boiling.   Artifi- 
cial Cooling.  Industrial  Applications 
vii 


viii  CONTENTS 

CHAPTER  PAGE 

XI.  THE  TRANSFERENCE  OF  HEAT 203 

Conduction.  Convection.  Radiation.  Heating  and  Ventilating 
XII.  MAGNETISM 214 

General  Properties  of  Magnets.   Terrestrial  Magnetism 

XIII.  STATIC  ELECTRICITY 225 

General  Facts  of  Electrification.  Distribution  of  Charge. 
Potential  and  Capacity 

XIV.  ELECTRICITY  IN  MOTION 244 

Detection  of  Electric  Currents.  Chemical  Effects.  Magnetic 
Effects.  Measurement  of  Currents.  Electric  Bell  and  Tele- 
graph. Resistance  and  Electromotive  Force.  Primary  Cells. 
Secondary  Cells.  Heating  Effects 

XV.  INDUCED  CURRENTS 290 

The  Principle  of  the  Dynamo  and  Motor.  Dynamos.  The 
Principle  of  the  Induction  Coil  and  Transformer 

XVI.  NATURE  AND  TRANSMISSION  OF  SOUND 319 

Speed  and  Nature.  Reflection,  Reenf orcement,  and  Interfer- 
ence 

XVII.  PROPERTIES  OF  MUSICAL  SOUNDS 337 

Musical  Scales.  Vibrating  Strings.  Fundamentals  and 
Overtones.  Wind  Instruments 

XVIII.  NATURE  AND  PROPAGATION  OF  LIGHT 357 

Transmission  of  Light.   The  Nature  of  Light 

XIX.  IMAGE  FORMATION 378 

Images  formed  by  Lenses.  Images  in  Mirrors.  Optical 
Instruments 

XX.  COLOR  PHENOMENA 402 

Color  and  Wave  Length.    Spectra 

XXI.  INVISIBLE  RADIATIONS 417 

Radiation  from  a  Hot  Body.  Electrical  Radiations.  Cathode 
and  Rontgen  Rays.  Radioactivity 

APPENDIX 447 

INDEX  .    465 


PORTRAITS  OF  PHYSICISTS  AND  ILLUSTRATIONS 
OF  RECENT  ACHIEVEMENTS  IN  PHYSICS 

PAGE 

1.  The  Navy-Curtiss  Hydroplane,  NC-4  (In  colors)     .    .    .     Frontispiece 

2.  Archimedes 22 

3.  The  Details  of  a  Submarine .    .    .  23 

4.  Otto  von  Guericke 32 

5.  The  Mercury-Diffusion  Air  Pump 33 

6.  British  Dirigible  Airship  R-34  Arriving  in  America 44 

7.  The  United  States  Army  Observation  Balloon 45 

8.  Galileo 72 

9.  French  340-mm.  Gun  in  Action 73 

10.  Sir  Isaac  Newton 84 

11.  The  Cream  Separator 85 

12.  James  Clerk-Maxwell 102 

13.  Heinrich  Rudolph  Hertz 102 

14.  A  Gas  Mask 103 

15.  James  Prescott  Joule 122 

16.  James  Watt 122 

17.  The  Rocket  and  the  Virginian  Mallet 123 

18.  Lord  Kelvin  (Sir  William  Thomson) 134 

19.  The  Clermont  and  the  Leviathan 135 

20.  A  United  States  Dreadnaught  in  the  Panama  Canal 152 

21.  The  Vickers-Vimy  Airplane 153 

22.  A  Tank 190 

23.  The  Liberty  Motor 191 

24.  Section  of  a  Modern  Automobile 198 

25.  The  Carburetor  and  an  Ignition  System        199 

26.  William  Gilbert 222 

27.  The  Sperry  Gyrocompass 223 

28.  Benjamin  Franklin <  230 

29.  Franklin's  Kite  Experiment 231 

30.  Count  Alessandro  Volta 240 

31.  A  Modern  High-Tension  Tower 241 

32.  Hans  Christian  Oersted 246 

33.  Joseph  Henry 246 

34.  Electromagnets 247 

ix 


X  LIST  OF  ILLUSTRATIONS 

PAGE 

35.  Andre"  Marie  Ampere 256 

36.  Huge  Rotor 257 

37.  Samuel  F.  B.  Morse 260 

38.  Diagrams  of  Morse  Telegraph 261 

39.  Georg  Simon  Ohm 268 

40.  The  Electric  Iron  and  Fuses 269 

41.  Michael  Faraday 290 

42.  Induction  Motor 291 

43.  Alexander  Graham  Bell 316 

44.  Thomas  A.  Edison 316 

45.  Guglielmo  Marconi 316 

46.  Orville  Wright 316 

47.  The  Original  Wright  Glider  and  the  First  Power-Driven  Airplane  317 

48.  Sound  Waves  of  Spoken  Words    . 346 

49.  Sound  Ranging  Record  of  the  End  of  the  War 347 

50.  A.  A.  Michelson 358 

51.  Lord  Rayleigh  (John  William  Strutt) 358 

52.  Henry  A.  Rowland .358 

53.  Sir  William  Crookes 358 

54.  X-Ray  Picture  of  the  Human  Thorax 359 

55.  Christian  Huygens 364 

56.  The  Great  Telescope  of  the  Yerkes  Observatory 365 

57.  Section  of  a  "  Movie  "  Film ' 386 

58.  Arthur  L.  Foley's  Sound-Wave  Photographs 387 

59.  Three-Color  Printing  (In  colors) 408 

60.  The  Wireless  Telephone  utilized  in  Aviation 424 

61.  Cinematograph  Film  of  a  Bullet  fired  through  a  Soap  Bubble     .    .  425 

62.  Alexanderson  High-Frequency  Alternator 428 

63.  Interior  of  Radio  Broadcasting  Station 429 

64.  Sir  Joseph  Thomson 440 

65.  Amplifier,  and  Diagram  of  Receiving  and  Amplifying  Set ....  441 

66.  William  Conrad  Rontgen 446 

67.  Antoine  Henri  Becquerel 446 

68.  Madame  Curie 446 

69.  E.  Rutherford 446 

70.  X-Ray  Spectra 447 


PRACTICAL  PHYSICS 

CHAPTER  I 

MEASUREMENT 
FUNDAMENTAL  UNITS 

1.  Introductory.    A  certain  amount  of  knowledge  about 
familiar  things  comes  to  us  all  very  early  in  life.    We  learn 
almost  unconsciously,  for  example,  that  stones  fall  and  bal- 
loons rise,   that  the  teakettle  stops  boiling  when  removed 
from  the  fire,  that  telephone  messages  travel  by  electric  cur- 
rents, etc.    The  aim  of  the  study  of  physics  is  to  set  us  to 
thinking  about  how  and  why  such  things  happen,  and,  to  a  less 
degree,  to  acquaint  us  with  other  happenings  which  we  may 
not  have  noticed  or  heard  of  previously. 

Most  of  our  accurate  knowledge  about  natural  phenomena 
has  been  acquired  through  careful  measurements.  We  can 
measure  three  fundamentally  different  kinds  of  quantities,  — 
length,  mass,  and  time,  —  and  we  shall  find  that  all  other 
measurements  may  be  reduced  to  these  three.  Our  first  prob- 
lem in  physics  is,  then,  to  learn  something  about  the  units  in 
terms  of  which  all  our  physical  knowledge  is  expressed. 

2.  The  historic  standard   of   length.    Nearly   all   civilized 
nations  have   at  some  time  employed   a  unit  of  length  the 
name   of  which  bore  the  same  significance  as  does  foot  in 
English.    There  can  scarcely  be  any  doubt,  therefore,  that  in 
each  country  this  unit  has  been  derived  from  the  length  of 

l 


2  MEASUREMENT 

the  human  foot.  It  is  probable  that  in  England,  after  the  yard 
(a  unit  which  is  supposed  to  have  represented  the  length  of 
the  arm  of  King  Henry  I)  became  established  as  a  standard, 
the  foot  was  arbitrarily  chosen  as  one  third  of  this  standard 
yard.  In  view  of  such  an  origin  it  will  be  clear  why  no  agree- 
ment existed  among  the  units  in  use  in  different  countries. 

3.  Relations  between  different  units  of  length.    It  has  also 
been  true,  in  general,  that  in  a  given  country  the  different 
units  of  length  in  common  use  (such,  for  example,  as  the 
inch,  the  hand,  the  foot,  the  fathom,  the  rod,  the  mile,  etc.) 
have  been  derived  either  from  the  lengths  of  different  mem- 
bers of  the  human  body  or  from  equally  unrelated  magni- 
tudes, and  in  consequence  have  been  connected  with  one 
another  by  different,  and  often  by  very  awkward,  multipliers. 
Thus,  there  are  12  inches  in  a  foot,  3  feet  in  a  yard,  5J  yards 
in  a  rod,  1760  yards  in  a  mile,  etc. 

4.  Relations  between  units  of  length,   area,  volume,   and 
mass.    A  similar  and  even  worse  complexity  exists  in  the  rela- 
tions of  the  units  of  length  to  those  of  area,  capacity,  and  mass. 
Thus,  there  are  272|  square  feet  in  a  square  rod ;  57|  cubic 
inches  in  a  quart,  and  31J  gallons  in  a  barrel.    Again,  the 
pound,  instead  of  being  the  mass  of  a  cubic  inch  or  a  cubic 
foot  of  water,  or  of  some  other  common  substance,  is  the  mass 
of  a  cylinder  of  platinum,  of  inconvenient  dimensions,  which 
is  preserved  in  London. 

5.  Origin  of  the  metric  system.    At  the  time  of  the  French 
Revolution  the  extreme  inconvenience  of  existing  weights  and 
measures,  together  with  the  confusion  arising  from  the  use  of 
different  standards  in  different  localities,  led  the  National 
Assembly  of  France  to  appoint  a  commission  to  devise  a  more 
logical  system.    The  result  of  the  labors  of  this  commission 
was  the  present  metric  system,  which  was  introduced  in  France 
in  1793  and  has  since  been  adopted  by  the  governments  of 
most  civilized  nations  except  those  of  Great  Britain  and  the 


FUNDAMENTAL  UNITS  3 

United  States ;  and  even  in  these  countries  its  use  in  scientific 
work  is  practically  universal.  The  World  War  has  done  much 
to  speed  its  adoption  in  these  countries. 

6.  The  standard  meter.  The  standard  length  in  the  metric 
system  is  called  the  meter.  It  is  the  distance,  at  the  freezing 
temperature,  between  two  transverse  parallel  lines  ruled  on 
a  bar  of  platmum-iridium  (Fig.  1),  which  is  kept  at  the 
International  Bureau  of  Weights  and  Measures  at  Sevres, 
near  Paris.  This  distance  is  39.37  inches. 

In  order  that  this  standard  length  might  be  reproduced  if 
lost,  the  commission  attempted  to  make  it  one  ten-millionth 


Exact  size  of 
the  cross  section 


FIG.  1.   The  standard  meter 

of  the  distance  from  the  equator  to  the  north  pole,  measured 
on  the  meridian  of  Paris.  But  since  later  measurements  have 
thrown  some  doubt  upon  the  exactness  of  the  commission's 
determination  of  this  distance,  we  now  define  the  meter,  not 
as  any  particular  fraction  of  the  earth's  quadrant,  but  simply 
as  the  distance  between  the  scratches  on  the  bar  mentioned 
above.  On  account  of  its  more  convenient  size,  the  centi- 
meter, one  one-hundredth  of  a  meter,  is  universally  used,  for 
scientific  purposes,  as  the  fundamental  unit  of  length. 

7.  Metric  standard  capacity.  The  standard  unit  of  capacity 
is  called  the  liter.  It  is  the  volume  of  a  cube  which  is  one  tenth 
of  a  meter  (about  4  inches)  on  a  side.  The  liter  is  therefore 


4  MEASUKEMEXT 

equal  to  1000  cubic  centimeters  (cc.).  It  is  equivalent  to  1.057 
quarts.  A  liter  and  a  quart  are  therefore  roughly  equivalent 
measures. 

8.  The  metric  standard  of  mass.    In  order  to  establish  a 
connection  between  the  unit  of  length  and  the  unit  of  mass, 
the  commission  directed  a  committee  of  the  French  Academy 
to  prepare  a  cylinder  of  platinum  which  should  have  the  same 
weight  as  a  liter  of  water  at  its  temperature  of  greatest  density, 
namely,  4°  Centigrade  (39°  Fahrenheit).   An  exact  equivalent 
of  this  cylinder,  made  of  platinum-iridium  and  kept  at  Sevres 
with  the  standard  meter,  now  represents  the  standard  of  mass 
in  the  metric  system.    It  is  called  the  standard  kilogram  and 
is  equivalent  to  about  2.2  pounds.   One  one-thousandth  of  this 
mass  was  adopted  as  the  fundamental  unit  of  mass  and  was 
named  the  gram.    For  practical  purposes,  therefore,  the  gram 
may  be  taken  as  equal  to  the  mass  of  one  cubic  centimeter  of  water, 

9.  The  other  metric  units.    The  three  standard  units  of  the 
metric  system  —  the  meter,  the  liter,  and  the  gram  —  have 
decimal  multiples  and  submultiples,  so  that  every  unit  of 
length,  volume,  or  mass  is  connected  with  the  unit  of  next 
higher  denomination  by  an  invariable  multiplier,  namely,  ten. 

The  names  of  the  multiples  are  obtained  by  adding  the 
Greek  prefixes,  deka  (ten),  hecto  (hundred),  kilo  (thousand)  ; 
while  the  submultiples  are  formed  by  adding  the  Latin  prefixes, 
deci  (tenth),  centi  (hundredth),  and  milli  (thousandth).  Thus  : 

1  dekameter  =  10  meters  1  decimeter   =  J_.  meter 

1  hectometer  =  100  meters  1  centimeter  =  -j-L  meter 

1  kilometer    =  1000  meters  1  millimeter  =  10100  meter 

The  most  common  of  these  units,  with  the  abbreviations 
which  will  henceforth  be  used  for  them,  are  the  following: 

meter  (m.)  millimeter  (mm.)  gram  (g.) 

kilometer  (km.)         liter  (1.)  kilogram  (kg.) 

centimeter  (cm.)        cubic  centimeter  (cc.)        milligram  (mg.) 


FUNDAMENTAL  UNITS  5 

10.  Relations  between  the  English  and  metric  units.    The 

following  table,   which  is   inserted  for  reference,  gives  the 
relation  between  the  most  common  English  and  metric  units. 

1  inch  (in.)  =  2.54  cm.  1  cm.  =  .3937  in. 

1  foot  (ft.)    =  30.48  cm.  1  m,    =  1.094  yd.  =  39.37  in. 

1  mile  (mi.)  =  1.609  km.  1  km.  =  .6214  mi. 

1  grain  =  64.8  mg.  1  g.      =  15.44  grains 

1  oz.  av.         =  28.35  g.  1  g.     =  .0353  oz. 

1  Ib.  av.         =  .4536  kg.  1  kg.  =  2.204  Ib. 

The  relations  1  in.  =  2.54  cm.,  1  m.  =  39.37  in.,  1  kilo 
(kg.)  =  2.2  Ib.,  1  km.  =  .62  mi.  should  be  memorized. 
Portions  of  a  centimeter  and  of  an  inch  scale  are  shown 
together  in  Fig.  2. 

11.  The  standard  unit  of  time.    The  second  is  taken  among 
all   civilized   nations    as   the   standard   unit   of   time.    It   is 
86400    part   of   the   time   from   noon    to   noon. 

12.  The  three  fundamental  units.    It  is  evident  that  meas- 
urements of  both  area  and  volume  may  be  reduced  simply 


CENTIMETER 

0123456 


UUU 


I  llll  IIJllJU 


1 1]  1 1   I)  I  I  PI  1 1 1  I]  I]  If]  I  IT 

0  INCH          1  2 

FIG.  2.    Centimeter  and  inch  scales 

to  measurements  of  length;  for  an  area  is  expressed  as  the 
product  of  two  lengths,  and  a  volume  as  the  product  of 
three  lengths.  For  these  reasons  the  units  of  area  and 
volume  are  looked  upon  as  derived  units,  depending  on  one 
fundamental  unit,  the  unit  of  length. 

Now  it  is  found  that  just  as  measurements  of  area  and 
of  volume  can  be  reduced  to  measurements  of  length,  so 
the  determination  of  any  measurable  quantities,  such  as  the 
pressure  in  a  steam  boiler,  the  velocity  of  a  moving  train. 


6  MEASUREMENT 

the  amount  of  electricity  consumed  by  an  electric  lamp,  the 
amount  of  magnetism  in  a  magnet,  etc.,  can  be  reduced 
simply  to  measurements  of  length,  mass,  and  time.  Hence 
the  centimeter,  the  gram,  and  the  second  are  considered  the  three 
fundamental  units.  Whenever  any  measurement  has  been 
reduced  to  its  equivalent  in  terms  of  centimeters,  grams, 
and  seconds,  it  is  said,  for  short,  to  be  expressed  in  C.G.S. 
(Centimeter-Gram-Second)  units. 

13.  Measurement  of  length.    Measuring  the   length  of  a 
body  consists  simply  in  comparing  its  length  with  that  of 
the  standard  meter  bar  kept  at  the  International  Bureau.    In 
order  that  this  may  be  done  conveniently,  great  numbers  of 
rods  of  the  same  length  as  this  standard  meter  bar  have  been 
made  and  scattered  all  over  the  world.    They  are  our  common 
meter  sticks.    They  are  divided  into  10,  100,  or  1000  equal 
parts,  great  care  being  taken  to  have  all  the  parts  of  exactly 
the  same  length.    The  method  of  making  a  measurement  with 
such  a  bar  is  more  or  less  familiar  to  everyone. 

14.  Measurement  of  mass.    Similarly,  measuring  the  mass 
of  a  body  consists  in  comparing  its  mass  with  that  of  the 
standard  kilogram.    In  order  that  this  might  be  done  con- 
veniently, it  was  first  necessary  to  construct  bodies  of  the 
same  mass  as  this  kilogram,  and  then  to  make  a  whole  series 
of  bodies  whose  masses  were  |,  -j^-,  y^-,  10100,  etc.  of  the 
mass  of  this  kilogram;  in  other  words,  to  construct  a  set  of 
standard  masses  commonly  called  a  set  of  weights. 

With  the  aid  of  such  a  set  of  standard  masses  the  deter- 
mination of  the  mass  of  any  unknown  body  is  made  by  first 
placing  the  body  upon  the  pan  A  (Fig.  3)  and  counterpoising 
with  shot,  paper,  etc.,  then  replacing  the  unknown  body  by 
as  many  of  the  standard  masses  as  are  required  to  bring  the 
pointer  back  to  0  again.  The  mass  of  the  body  is  equal  to 
the  sum  of  these  standard  masses.  This  rigorously  correct 
method  of  weighing  is  called  the  method  of  substitution. 


FUNDAMENTAL  UNITS 


If  a  balance  is  well  constructed,  however,  a  weighing  may 
usually  be  made  with  sufficient  accuracy  by  simply  placing 
the  unknown  body  upon  one 
pan  and  finding  the  sum  of 
the  standard  masses  which 
must  then  be  placed  upon 
the  other  pan  to  bring  the 
pointer  again  to  0.  This  is 
the  usual  method  of  weighing. 
It  gives  correct  results,  how- 
ever, only  when  the  knife-edge 
0  is  exactly  midway  between 
the  points  of  support  m  and 
n  of  the  two  pans.  The  method  of  substitution,  on  the  other 
hand,  is  independent  of  the  position  of  the  knife-edge.  It  is 
customary  to  consider  that  the  mass  of  a  body  determined  as  here 
indicated  is  a  measure  of  the  quantity  of  matter  which  it  contains. 


FIG.  3.   The  simple  balance 


QUESTIONS  AND  PROBLEMS 

1.  The  200-meter  run  at  the  Olympic  games  corresponds  to  the  220- 
yard  run  in  our  local  games.    Which  is  the  longer  and  how  much  ? 

2.  The  French  75-mm.  guns  have  what  diameter  in  inches  ? 

3.  The  Twentieth  Century  Limited  runs  from  New  York  to  Chicago 
(967  mi.)  in  20  hr.    Find  its  average  speed  in  miles  per  hour. 

4.  Name  as  many  advantages  as  you  can  which  the  metric  system 
has  over  the  English  system.    Can  you  think  of  any  disadvantages  ? 

5.  What  must  you  do  to  find  the  capacity  in  liters  of  a  box  when 
its  length,  breadth,  and  depth  are  given  in  meters  ?  to  find  the  capacity 
in  quarts  when  its  dimensions  are  given  in  feet? 

6.  Find  the  number  of  millimeters  in  6  km.    Find  the  number  of 
inches  in  4  mi.    Which  is  the  easier? 

7.  With  a  Vickers-Vimy  biplane  Captain  Alcock  and  Lieutenant 
Brown  completed,  on  June  15, 1919,  the  first  nonstop  transatlantic  flight 
of  1890  miles  frojn  Newfoundland  to  Ireland  in  15  hr.  57  min.    How 
many  miles  per  hour?    How  many  kilometers  per  hour? 

8.  Find  the  capacity  in  liters  of  a  box  .5  m.  long,  20  cm.  wide,  and 
100  mm.  deep. 


8  MEASUREMENT 

DENSITY 

15.  Definition  of  density.  When  equal  volumes  of  different 
substances,  such  as  lead,  wood,  iron,  etc.,  are  weighed  in  the 
manner  described  above,  they  are  found  to  have  widely  differ- 
ent masses.  The  term  "  density  "  is  used  to  denote  the  mass, 
or  quantity  of  matter,  per  unit  volume. 

Thus,  for  example,  in  the  English  system  the  cubic  foot  is 
the  unit  of  volume  and  the  pound  the  unit  of  mass.  Since  1  cubic 
foot  of  water  is  found  to  weigh  62.4  pounds,  we  say  that  in  the 
English  system  the  density  of  water  is  62.4  pounds  per  cubic  foot. 

In  the  C.G.S.  system  the  cubic  centimeter  is  taken  as  the 
unit  of  volume  and  the  gram  as  the  unit  of  mass.  Hence  we 
say  that  in  this  system  the  density  of  water  is  1  gram  per 
cubic  centimeter,  for  it  will  be  remembered  that  the  gram  was 
taken  as  the  mass  of  1  cubic  centimeter  of  water.  Unless 
otherwise  expressly  stated,  density  is  now  universally  under- 
stood to  mean  density  in  C.G.S.  units;  that  is,  the  density  of  a 
substance  is  the  mass  in  grams  of  1  cubic  centimeter  of  that  sub- 
stance. For  example,  if  a  block  of  cast  iron  3  cm.  wide,  8  cm. 
long,  and  1  cm.  thick  weighs  177.6  g.,  then,  since  there  are 
24  cc.  in  the  block,  the  mass  of  1  cc.,  that  is,  the  density,  is 
equal  to  — |^-,  or  7.4  g.  per  cubic  centimeter. 

The  density  of  some  of  the  most  common  substances  is  given 
in  the  following  table  : 

DENSITIES  OF  SOLIDS 

(In  grams  per  cubic  centimeter) 

Aluminium 2.58       Nickel 8.9 

Brass 8.5        Oak 8 

Copper 8.9         Pine 5 

Cork 24       Platinum 21.4 

Glass 2.6         Silver 10.5 

Gold 19.3         Tin 7.3 

Iron  (cast) 7.4         Tungsten 19.6 

Lead                                        .  11.3  Zinc .                                              7.1 


DENSITY  9 

DENSITIES  OF  LIQUIDS 

(In  grams  per  cubic  centimeter) 

Alcohol 79       Hydrochloric  acid     .     .     „       1.27 

Carbon  bisulphide       .     .     .     1.29       Mercury 13.6 

Glycerin  ..'.'. 1.26       Gasoline 75 

16.  Relation  between  mass,  volume,  and  density.    Since  the 
mass  of  a  body  is  equal  to  the  total  number  of  grams  which 
it  contains,  and  since  its  volume  is  the  number  of  cubic  centi- 
meters which  it  occupies,  the  mass  of  1  cubic  centimeter  is 
evidently  equal  to  the  total  mass  divided  by  the  volume.   Thus, 
if  the  mass  of  100  cubic  centimeters  of  iron  is  740  grams,  the 
density  of  iron  must  equal  740  -f-100  =  7.4  grams  to  the  cubic 
centimeter.    To  express  this  relation  in  the  form  of  an  equa- 
tion, let  M  represent  the  mass  of  a  body,  that  is,  its  total 
number  of  grams ;  V  its  volume,  that  is,  its  total  number  of 
cubic  centimeters ;  and  D  its  density,  that  is,  the  number  of 
grams  in  1  cubic  centimeter;  then 

»-f  m 

This  equation  merely  states  the  definition  of  density  in 
algebraic  form. 

17.  Distinction  between  density  and  specific  gravity.    The 
term  "  specific  gravity  "  is  used  to  denote  the  ratio  between  the 
weight  of  a  body  and  the  weight  of  an  equal  volume  of  water.* 

Thus,  if  a  certain  piece  of  iron  weighs  7.4  times  as  much 
as  an  equal  volume  of  water,  its  specific  gravity  is  7.4.  But 
since  the  density  of  water  in  C.G.S.  units  is  1  gram  per  cubic 
centimeter,  the  density  of  iron  in  that  system  is  7.4  grams 
per  cubic  centimeter.  It  is  clear,  then,  that  density  in  0.  G-.S. 
units  is  numerically  the  same  as  specific  gravity. 

*  For  the  present  purpose  the  terms  "weight"  and  "mass"  may  be  used 
interchangeably.  They  are  in  general  numerically  equal,  although  an  impor- 
tant distinction  between  them  will  be  developed  in  §  73.  Weight  is  in  reality 
a  force  rather  than  a  quantity  of  matter. 


10  MEASUREMENT 

Specific  gravity  is  the  same  in  all  systems,  since  it  simply 
expresses  how  many  times  as  heavy  as  an  equal  volume  of  water 
a  body  is.  Density,  however,  which  we  have  defined  as  the 
mass  per  unit  volume,  is  different  in  different  systems.  Thus, 
in  the  English  system  the  density  of  iron  is  462  pounds  per 
cubic  foot  (7.4  x  62.4),  since  we  have  found  that  water  weighs 

62.4  pounds  per  cubic  foot  and  that  iron  weighs  7.4  times  as 
much  as  an  equal  volume  of  water.* 

QUESTIONS  AND  PROBLEMS  t 

1.  A  liter  of  milk  weighs  1032  grams.    What  is  its  density  and  its 
specific  gravity  ? 

2.  A  ball  of  yarn  was  squeezed  into  £  of  its  original  bulk.    What 
effect  did  this  produce  upon  its  mass,  its  volume,  and  its  density  ? 

3.  If  a  wooden  beam  is  30  X  20  x  500  cm.  and  has  a  mass  of  150  kg., 
what  is  the  density  of  wood  ? 

4.  Would  you  attempt  to  carry  home  a  block  of  gold  the  size  of  a 
peck  measure?    (Consider  a  peck  equal  to  8  1.    See  table,  p.  8.) 

5.  What  is  the  mass  of  a  liter  of  alcohol? 

6.  How  many  cubic  centimeters  in  a  block  of  brass  weighing  34  g.? 

7.  What  is  the  weight  in  metric  tons  of  a  cube  of  lead  2  m.  on  an 
edge  ?    (A  metric  ton  is  1000  kilos,  or  about  2200  Ib.) 

8.  Find  the  volume  in  liters  of  a  block  of  platinum  weighing 

45.5  kilos. 

9.  One  kilogram  of  alcohol  is  poured  into  a  cylindrical  vessel  and 
fills  it  to  a  depth  of  8  cm.    Find  the  cross  section  of  the  cylinder. 

10.  Find  the  length  of  a  lead  rod  1  cm.  in  diameter  and  weighing  1  kg. 

*  Laboratory  exercises  on  length,  mass,  and  density  measurements  should 
accompany  or  follow  this  chapter.  See,  for  example,  Experiments  1,  2,  and  3 
of  the  authors'  Manual. 

t  Questions  and  problems  to  supplement  this  chapter  and  all  following 
chapters  are  given  in  the  Appendix,  page  447. 


CHAPTER  II 

PRESSURE  IN  LIQUIDS 

LIQUID  PRESSURE  BEKEATH  A  FREE  SURFACE 

18.  Force   beneath  the   surface  of  a  liquid.    We  are   all 

conscious  of  the  fact  that  in  order  to  lift  a  kilogram  of  mass 
we  must  exert  an  upward  pull.  Experience  has  taught  us 
that  the  greater  the  mass,  the  greater  the  force  which  we 
must  exert.  The  force  is  commonly  taken  as  numerically 
equal  to  the  mass  lifted.  This  is  called  the  weight  measure  of 
a  force.  A.  push  or  pull  which  is  equal  to  that  required  to  sup- 
port a  gram  of  mass  is  called  a  gram  of  force.  Thus,  five  grams 
of  force  are  needed  to  lift  a  new  five-cent  piece. 

To  investigate  the  nature  of  the  forces  beneath  the  free  surface  of  a 
liquid  we  shall  use  a  pressure  gauge  of  the  form  shown  in  Fig.  4.  If 
the  rubber  diaphragm  which  is  stretched  across  the  mouth  of  a  thistle 
tube  A  is  pressed  in  lightly  with  the  finger,  the  drop  of  ink  B  will  be 
observed  to  move  forward  in  the  tube  T,  but  it  will  return  again  to  its 
first  position  as  soon  as  the  finger  is  removed.  If  the  pressure  of  the 
finger  is  increased,  the  drop  will  move  forward  a  greater  distance  than 
before.  We  may  therefore  take  the  amount  of  motion  of  the  drop  as  a 
measure  of  the  force  acting  on  the  diaphragm. 

Now  let  A  be  pushed  down  first  2  cm.,  then  4  cm.,  then  8  cm.  below 
the  surface  of  the  water  *(Fig.  4).  The  motion  of  the  index  B  will  show 
that  the  upward  force  continually  increases  as  the  depth  increases. 

Careful  measurements  made  in  the  laboratory  will  show 
that  the  force  is  directly  proportional  to  the  depth.* 

*  It  is  recommended  that  quantitative  laboratory  work  on  the  law  of 
depths  and  on  the  use  of  manometers  accompany  this  discussion.  See,  for 
example,  Experiments  4  and  5  of  the  authors'  Manual. 

11 


12  PKESSUKE  IN  LIQUIDS 

Let  the  diaphragm  A  (Fig.  4)  be  pushed  down  to  some  convenient 
depth  (for  example,  10  centimeters)  and  the  position  of  the  index  noted. 
Then  let  it  be  turned  sidewise  so  that  its  plane  is  vertical  (see  a,  Fig.  4), 
and  adjusted  in  position  until  its  center  is  exactly  10  centimeters  beneath 
the  surface,  that  is,  until  the 
average  depth  of  the  diaphragm 
is  the  same  as  before.  The 
position  of  the  index  will  show 
that  the  force  is  also  exactly  Fm  4  Qauge  for  measuri  liquid 
the  same  as  before.  pressure 

Let  the  diaphragm  then  be 

turned  to  the  position  Z>,  so  that  the  gauge  measures  the  downward  force 
at  a  depth  of  10  centimeters.  The  index  will  show  that  this  force  is 
again  the  same. 

We  conclude,  therefore,  that  at  a  given  depth  a  liquid 
presses  up  and  down  and  sidewise  on  a  given  surface  with 
exactly  the  same  force. 

19.  Magnitude  of  the  force.  If  a  vessel  like  that  shown 
in  Fig.  5  is  filled  with  a  liquid,  the  force  against  the  bottom 
is  obviously  equal  to  the  weight  of  the  column  of 
liquid  resting  upon  the  bottom.  Thus,  if  F  repre- 
sents this  force  in  grams,  A  the  area  in  square  centi- 
meters, h  the  depth  in  centimeters,  and  d  the  density 
in  grams  per  cubic  centimeter,  we  shall  have 

F=Ahd.  (1)     FIG.  5 

Since,  as  was  shown  by  the  experiment  of  the  preceding 
section,  the  force  is  the  same  in  all  directions  at  a  given 
depth,  we  have  the  following  general  rule : 

Tlie  force  which  a  liquid  exerts  against  any  surface  is  equal 
to  the  area  of  the  surface  times  its  average  depth  times  the  density 
of  the  liquid. 

It  is  important  to  remember  that  "  average  depth  "  means 
the  vertical  distance  from  the  level  of  the  free  surface  to  the 
center  of  the  area  in  question. 


PRESSURE  BENEATH  A  FREE  SURFACE 


13 


20.  Pressure  in  liquids.  Thus  far  attention  has  been  con- 
fined to  the  total  force  exerted  by  a  liquid  against  the  whole 
of  a  given  surface.  It  is  often  more  convenient  to  imagine 
the  surface  divided  into  square  centimeters  or  square  inches, 
and  then  to  consider  the  force  on  one  of  these  units  of  area. 
In  physics  the  word  "  pressure  "  is  used  exclusively  to  denote 
the  force  per  unit  area.  Pressure  is  thus  a  measure  of  the 
intensity  of  the  force  acting  on  a  surface,  and  does  not  de- 
pend at  all  on  the  area  of  the  surface.  Since,  by  §  19,  F=  Ahd, 
and  since  by  definition  the  pressure  p  is  equal  to  the  force 
per  unit  area,  we  have 

(2) 


~ 


Therefore  the  pressure  at  a  depth  of  h  centimeters  below  the 
surface  of  a  liquid  of  density  d  is  hd  grams  per  square  centimeter. 

If  the  height  is  given  in  feet  and  the  density  in  pounds  per 
cubic  foot,  then  the  product  hd  gives  pressure  in  pounds 
per  square  foot.  Dividing  by  144  gives  the  result  in  pounds 
per  square  inch. 

21.  Levels  of  liquids  in  connecting  vessels.  It  is  a  perfectly 
familiar  fact  that  when  water  is  poured  into  a  teapot  it  stands 
at  exactly  the  same  level  in 
the  spout  as  in  the  body  of 
the  teapot ;  or  if  it  is  poured 
into  a  number  of  connected 
vessels  like  those  shown  in 
Fig.  6,  the  surfaces  of  the 
liquid  in  the  various  vessels 
lie  in  the  same  horizontal 
plane.  Now  the  pressure  at 
c  (Fig.  7)  was  shown  by  the 
experiment  of  §  18  to  be 
equal  to  the  density  of  the  liquid  times  the  depth  eg.  The 
pressure  at  o  in  the  opposite  direction  must  be  equal  to 


FIG.  6.   Water  level  in  communi- 
cating vessels 


14 


PBESSUKE  IN  LIQUIDS 


that  at  c,  since  the  liquid  does  not  tend  to  move  in  either 
direction.  Hence  the  pressure  at  o  must  be  ks  times  the  density. 

If  water  is  poured  in  at  s  so  that  the 
height  Jcs  is  increased,  the  pressure  to 
the  left  at  o  becomes  greater  than  the 
pressure  to  the  right  at  <?,  and  a  flow  of 
water  takes  place  to  the  left  until  the 
heights  are  again  equal. 

It  follows  from  these  observations 
on  the  level  of  water  in  connected 


FIG.  7.   Why  water  seeks 
its  level 


vessels   that   the  pressure   beneath   the 

surface  of  a  liquid  depends  simply  on  the  vertical  depth  beneath 

the  free  surface,  and  not  at  all  on  the  size  or  shape  of  the  vessel. 


QUESTIONS  AND  PROBLEMS 

1.  Soundings  at  sea  are  made  by  lowering  some  kind  of  pressure 
gauge.    When  this  gauge  reads  1.3  kg.  per  square  centimeter,  what  is 
the  depth?    (Density  of  sea  water=1.026.) 

2.  Kerosene  is  0.8  as  heavy  as  water  (1  cu.  ft.  of  water=62.4  lb.). 
Find  the  pressure  of  the  kerosene  per  square  foot  and  per  square  inch 
on  the  bottom  of  an  oil  tank  filled  to  a  depth  of  30  ft. 

3.  What  pressure  per  square  inch  is  required  to  force  water  to  the 
top  of  the  Woolworth  building  in  New  York  City,  780  ft.  high  ? 

4.  A  swimming  tank  50  ft.  square  is  filled  with  water  to  a  depth  of 
5  ft.   Find  the  force  of  the  water  on  the  bottom ;  on  one  side. 

5.  If  the  areas  of  the  surfaces  AB  in 
Fig.  8,  (1)  and  (#),  are  the  same,  and  if 
water  is  poured  into  each  vessel  at  D  till 
it  stands  at  the  same  height  above  AB, 
how  will  the  downward  force  on  A  B  in 
Fig.  8,  (#),  compare  with  that  in  Fig.  8, 
(1)?  Test  your  answer,  if  possible,  by 

making  AB  a  piece  of  cardboard  and         FIG.  8.   Illustrating  hydro- 
pouring   water  in   at  D,  in  each  case,  static  paradox 
until  the  cardboard  is  forced  off. 

6.  If  the  vessel  shown  in  Fig.  10,  (.?)  (p.  15),  has  a  base  of  200  sq.  cm. 
and  if  the  water  stands  100  cm.  deep,  what  is  the  total  force  on  the 
bottom  ? 


PASCAL'S  LAW 


15 


7.  If  the  weight  of  the  empty  vessel  in  Fig.  10,  (I),  is  small  compared 
with  the  weight  of  the  contained  water,  will  the  force  required  to  lift 
the  vessel  and  water  be  greater  or  less  than  the  force 

exerted  by  the  water  against  the  bottom  ?  Explain. 

8.  A  whale  when  struck  with  a  harpoon  will  often 
dive  straight  down  as  much  as  400  fathoms  (2400  ft.). 
If  the  body  has  an  area  of  1000  sq.  ft.,  what  is  the  total 
force  to  which  it  is  subjected  ? 

9.  A  hole  5  cm.  square  is  made  in  a  ship's  bottom 
7  m.  below  the  water  line.    What  force  in  kilograms  is 
required  to  hold  a  board  above  the  hole? 

10.  Thirty  years  ago  standpipes  were  generally 
straight  cylinders.  To-day  they  are  more  commonly 
of  the  form  shown  in  Fig.  9.  What  are  the  advantages 
of  each  form  ? 


PASCAL'S  LAW 


FIG.  9.  A  water 
reservoir 


22.  Transmission    of    pressure    by    liquids. 

From  the  fact  that  pressure  within  a  free  liquid 
depends  simply  upon  the  depth  and  density  of  'the  liquid,  it 
is  possible  to  deduce  a  very  surprising  conclusion,  which  was 
first  stated  by  the  famous  French  scientist,  mathematician,  and 
philosopher,  Pascal  (1623-1662). 
Let  us  imagine  a  vessel  of  the 
shape  shown  in  Fig.  10,  (J),  to  be 
filled  with  water  up  to  the  level 
db.  For  simplicity  let  the  upper 
portion  be  assumed  to  be  1  square 
centimeter  in  cross  section.  Since 
the  density  of  water  is  1,  the  force 
with  which  it  presses  against  any 
square  centimeter  of  the  interior 
surface  which  is  li  centimeters 
beneath  the  level  ab  is  h  grams. 
Now  let  1  gram  of  water  (that  is,  1  cubic  centimeter)  be 
poured  into  the  tube.  Since  each  square  centimeter  of  sur- 
face, which  before  was  h  centimeters  beneath  the  level  of  the 


A 

a 

— 

* 

a 

= 

^ 

(1) 

f 

<*) 

5 

_s 

i^^. 

p 

^£ 

l-———C-= 

i 

i 

s 

FIG.  10.    Proof  of  Pascal's  law 


16,  PEESSUEE  IN  LIQUIDS 

water  in  the  tube,  is  now  A+l  centimeters  beneath  this  level, 
the  new  pressure  which  the  water  exerts  against  it  is  7i-fl 
grams ;  that  is,  applying  1  gram  of  force  to  the  square  cen- 
timeter of  surface  ab  has  added  1  gram  to  the  force  exerted 
by  the  liquid  against  each  square  centimeter  of  the  interior 
of  the  vessel.  Obviously  it  can  make  no  difference  whether 
the  pressure  which  was  applied  to  the  surface  ab  was  due 
to  a  weight  of  water  or  to  a  piston  carrying  a  load,  as  in 
Fig.  10,  (^),  or  to  any  other  cause  whatever.  We  thus  arrive 
at  Pascal's  conclusion  that  pressure  applied  anywhere  to  a  l>ody 
of  confined  liquid  is  transmitted  undiminished  to  every  portion 
of  the  surface  of  the  containing  vessel. 

23.  Multiplication  of  force  by  the  transmission  of  pressure 
by  liquids.    Pascal  himself  pointed  out  that  with  the  aid  of 
the  principle  stated  above  we  ought  to  be  able  to  transform 
a  very  small  force  into  one  of  un-  1J^2M 
limited    magnitude.      Thus,    if    the       !?              . 

area    of   the   cylinder   ab    (Fig.  11)     aw> 

is  1  sq.  cm.,  while  that  of  the  cylin-       F- 

der  AB  is  1000  sq.  cm.,  a  force  of      FIG.  11.  Multiplication  of 

1  kg.  applied  to  ab  would  be  trans-      force  by  transmission  of 

,  ,  pressure 

mitted  by  the  liquid  so  as  to  act  with 

a  force  of  1  kg.  on  each  square  centimeter  of  the  surface  AB. 
Hence  the  total  upward  force  exerted  against  the  piston  AB 
by  the  1  kg.  applied  at  ab  would  be  1000  kg.  Pascal's  own 
words  are  as  follows :  "  A  vessel  full  of  water  is  a  new  prin- 
ciple in  mechanics,  and  a  new  machine  for  the  multiplication 
of  force  to  any  required  extent,  since  one  man  will  by  this 
means  be  able  to  move  any  given  weight." 

24,  The  hydraulic  press.    The  experimental  proof  of  the  correctness 
of  the   conclusions  of   the  preceding  paragraph   is  furnished  by  the 
hydraulic  press,  an  instrument  now  in  common  use  for  subjecting  to 
enormous  pressures  paper,  cotton,  etc.  and  for  punching  holes  through 
iron  plates,  testing  the  strength  of   iron  beams,  extracting  oil  from 


PASCAL'S  LAW 


17 


seeds,  making  dies,  embossing  metal,  etc.  Hydraulic  presses  of  great 
power  have  been  designed  for  use  in  steel  works  to  replace  huge  steam 
hammers.  Compressing  forces  of  10,000  tons  or  more  are  thus  obtained. 
Much  cold  steel,  as  well  as  hot,  is  now  pressed  instead  of  hammered. 
Such  a  press  is  represented  in  section  in  Fig.  12.  As  the  small  piston 
p  is  raised,  water  from  the  cistern  C  enters  the  piston  chamber  through 
the  valve  v.  As  soon 
as  the  downstroke 
begins,  the  valve  v 
closes,  the  valve  v' 
opens,  and  the  pres- 
sure applied  on  the 
piston  p  is  trans- 
mitted through  the 
tube  K  to  the  large 
reservoir,  where  it 
acts  on  the  large 
cylinder  P. 

The  force  exerted 
upon  P  is  as  many 
times  that  applied 
to  p  as  the  area  of 
P  is  times  the  area 
OJ  P-  FIG.  12.  Diagram  of  a  hydraulic  press 

25.  No  gain  in  the  product  of  force  times  distance.  It  should 
be  noticed  that,  while  the  force  acting  on  AB  (Fig.  11)  is 
1000  times  as  great  as  the  force  acting  on  ab,  the  distance 
through  which  the  piston  AB  is  pushed  up  in  a  given  time  is 
but  YoVo  °^  the  distance  through  which  the  piston  ab  moves 
down.  For  forcing  ab  down  a  distance  of  1  centimeter  crowds 
but  1  cubic  centimeter  of  water  over  into  the  large  cylinder,  and 
this  additional  cubic  centimeter  can  raise  the  level  of  the  water 
there  but  10100  centimeter.  We  see,  therefore,  that  the  product 
of  the  force  acting  by  the  distance  moved  is  precisely  the  same 
at  both  ends  of  the  machine.  This  important  conclusion  will 
be  found  in  our  future  study  to  apply  to  all  machines. 


18 


PEESSUEE  IN  LIQUIDS 


26.  The  hydraulic  elevator.  Another  very  common  application  of 
the  principle  of  transformation  of  pressure  by  liquids  is  found  in  the 
hydraulic  elevator.  The  simplest  form  of  such  an  elevator  is  shown  in 
Fig.  13.  The  cage  A  is  borne  on  the  top  of  a  long  piston  P  which  runs 
in  a  cylindrical  pit  C  of  the  same  depth  as  the  height  to  which  the 
carriage  must  ascend. 
Water  enters  the  pit 
either  directly  from 
the  water  mains,  m, 
of  the  city's  supply  or, 
if  this  does  not  fur- 
nish sufficient  pres- 
sure, from  a  special 
reservoir  on  top  of 
the  building.  When 
the  elevator  boy  pulls 
up  on  the  cord  cc,  the 
valve  v  opens  so  as 
to  make  connection 
from  m  into  C.  The 
elevator  then  ascends. 
When  cc  is  pulled 
down,  v  turns  so  as  to 
permit  the  water  in 
C  to  escape  into  the 
sewer.  The  elevator 
then  descends. 

Where  speed  is  re- 
quired the  motion  of 
the  piston  is  com- 
municated indirectly 
to  the  cage  by  a  sys- 
tem of  pulleys  like 
that  shown  in  Fig.  14. 
With  this  arrangement  a  foot  of  upward  motion  of  the  piston  P 
causes  the  counterpoise  D  of  the  cage  to  descend  2  feet,  for  it  is  clear 
from  the  figure  that  when  the  piston  goes  up  1  foot,  enough  rope  must 
be  pulled  over  the  fixed  pulley  p  to  lengthen  each  of  the  two  strands  a 
and  b  1  foot.  Similarly,  when  the  counterpoise  descends  2  feet,  the  cage 
ascends  4  feet.  Hence  the  cage  moves  four  times  as  fast  and  four  times 


FIG. 14 

Diagrams  of  hydraulic  elevators 


PASCAL'S  LAW 


19 


as  far  as  the  piston.  The  elevators  in  the  Eiffel  Tower  in  Paiis  are 
of  this  sort.  They  have  a  total  travel  of  420  feet  and  are  capable  of 
lifting  50  people  400  feet  per  minute.  The  cylinder  C  and  piston  P  are 
often  not  in  a  pit  but  lie  in  a  horizontal  position.  Most  modern  eleva- 
tors are  electric  rather  than  hydraulic. 

27.  City  water  supply.  Fig.  15  illustrates  the  method  by 
which  a  city  is  often  supplied  with  water  from  a  distant  source. 
The  aqueduct  from  the  lake  a  passes  under  a  road  r,  a  brook 
^  and  a  hill  //,  and  into  a  reservoir  e,  from  which  it  is  forced 
by  the  pump  p  into  the  standpipe  P,  whence  it  is  distributed 
to  the  houses  of  the  city.  If  a  static  condition  prevailed  in 


FIG.  15.    City  water  supply  from  lake 

the  whole  system,  then  the  water  level  in  e  would  of  neces- 
sity be  the  same  as  that  in  a,  and  the  level  in  the  pipes  of 
the  building  B  would  be  the  same  as  that  in  the  standpipe  P. 
But  when  the  water  is  flowing,  the  friction  of  the  mains 
causes  the  level  in  e  to  be  somewhat  less  than  that  in  a,  and 
that  in  B  less  than  that  in  P.  It  is  on  account  of  the  friction 
both  of  the  air  and  of  the  pipes  that  the  fountain  /  does  not 
rise  nearly  as  high  as  the  ideal  limit  shown  in  the  figure. 

QUESTIONS  AND  PROBLEMS 

1.  A  jug  full  of  water  may  often  be  burst  by  striking  a  blow  on 
the  cork.    If  the  surface  of  the  jug  is  200  sq.  in.  and  the  cross  section  of 
the  cork  1  sq.  in.,  what  total  force  acts  on  the  interior  of  the  jug  when 
a  10-lb.  blow  is  struck  on  the  cork? 

2.  How  does  your  city  get  its  water?   How  is  the  pressure  in  the 
pipes  maintained? 


20  PRESSUEE  IN  LIQUIDS 

3.  If  the  water  pressure  in  the  city  mains  is  70  Ib.  to  the  square  inch, 
how  high  above  the  town  is  the  top  of  the  water  in  the  standpipe  ? 

4.  The  cross-sectional  areas  of  the  pistons  of  a  hydraulic  press  were 
3  sq.  in.  and  60  sq.  in.    How  great  a  weight  would  the  large  piston 
sustain  if  75  Ib.  were  applied  to  the  small  one  ? 

5.  The  diameters  of  the  pistons  of  a  hydraulic  press  were  2  in.  and 
20  in.    What  force  would  be  produced  upon  the  large  piston  by  50  Ib. 
on  the  small  one  ? 

6.  The  water  pressure  in  the  city  mains  is  80  Ib.  to  the  square  inch. 
The  diameter  of  the  piston  of  a  hydraulic  elevator  of  the  type  shown 
in  Fig.  13  is  10  in.    If  friction  could  be  disregarded,  how  heavy  a  load 
could  the  elevator  lift?  If  30%  of  the  ideal  value  must  be  allowed  for 
frictional  loss,  what  load  will  the  elevator  lift? 

7.  Suppose  a  tube  5  mm.  square  and  200  cm.  long  is  inserted  into  the 
top  of  a  box  20  cm.  on  a  side  and  filled  with  water ;  what  will  be  the 
total  force  on  the  bottom  of  the  box  ?   on  the  top  ? 


THE  PRINCIPLE  OF  ARCHIMEDES* 

28.  Apparent  loss  of  weight  of  a  body  in  a  liquid.  The 
preceding  experiments  have  shown  that  an  upward  force  acts 
against  the  bottom  of  any  body  immersed  in  a  liquid.  If 
the  body  is  a  boat,  cork,  piece  of  wood,  or  any  body  which 
floats,  it  is  clear  that,  since  it  is  in  equilibrium,  this  upward 
force  must  be  equal  to  the  weight  of  the  body.  Even  if  the 
body  does  not  float,  everyday  observation  shows  that  it  still 
loses  a  portion  of  its  natural  weight,  for  it  is  well  known 
that  it  is  easier  to  lift  a  stone  under  water  than  in  air,  or, 
again,  that  a  man  in  a  bathtub  can  support  his  whole  weight 
by  pressing  lightly  against  the  bottom  with  his  fingers.  It 
was  indeed  this  very  observation  which  first  led  the  old 
Greek  philosopher  Archimedes  (287-212  B.C.)  (see  opposite 
page  22)  to  the  discovery  of  the  exact  law  which  governs 
the  loss  of  weight  of  a  body  in  a  liquid. 

*  A  laboratory  exercise  on  the  experimental  proof  of  Archimedes'  princi- 
ple should  either  precede  or  accompany  this  discussion.  See,  foi  example, 
Experiment  6  of  the  authors1  Manual. 


THE  PRINCIPLE  OF  ARCHIMEDES  21 

Hiero,  the  tyrant  of  Syracuse,  had  ordered  a  gold  crown 
made,  but  suspected  that  the  artisan  had  fraudulently  used 
silver  as  well  as  gold  in  its  construction.  He  ordered  Archi- 
medes to  discover  whether  or  not  this  were  true.  How  to  do 
so  without  destroying  the  crown  was  at  first  a  puzzle  to  the 
old  philosopher.  While  in  his  daily  bath,  noticing  the  loss  of 
weight  of  his  own  body,  it  suddenly  occurred  to  him  that 
any  body  immersed  in  a  liquid  must  apparently  lose  a  loeight 
equal  to  the  weight  of  the  displaced  liquid.  He  is  said  to  have 
jumped  at  once  to  his  feet  and  rushed  through  the  streets 
of  Syracuse  crying,  "  Eureka !  Eureka !  "  (I  have  found  it !  I 
have  found  it!) 

29.  Theoretical  proof  of  Archimedes*  principle.    It  is  prob- 
able that  Archimedes,  with  that  faculty  which  is  so  common 
among  men  of  great  genius,  saw  the  truth  of  his  conclusion 
without  going .  through  any  logical  process 
of  proof.    Such  a  proof,  however,  can  easily 
be  given.   Thus,  since  the  upward  force  on 
the  bottom  of  the  block  abed  (Fig.  16)  is 
equal  to  the  weight  of  the  column  of  liquid 
obce,  and  since  the  downward  force  on  the 
top  of  this  block  is  equal  to  the  weight  of 

the  column  of  liquid  oade,  it  is  clear  that     FlG: 16'  Proof  that 

an  immersed  body 
the  upward  force  must  exceed  the  down-     js  buoyed  up  by  a 

ward  force    by  the  weight  of  the  column     force  equal  to  the 
of  liquid  abed.    Archimedes'  principle  may     wei£ht  of  the  dis- 

J  placed  liquid 

be  stated  thus: 

The  buoyant  force  exerted  by  a  liquid  is  exactly  equal  to  the 
weight  of  the  displaced  liquid. 

The  reasoning  is  exactly  the  same,  no  matter  what  may  be 
the  nature  of  the  liquid  in  which  the  body  is  immersed,  nor 
how  far  the  body  may  be  beneath  the  surface.  Further,  if  the 
body  weighs  more  than  the  liquid  which  it  displaces,  it  must 


22 


PKESSUKE  IN  LIQUIDS 


sink,  for  it  is  urged  down  with  the  force  of  its  own  weight, 
and  up  with  the  lesser  force  of  the  weight  of  the  displaced 
liquid.  But  if  it  weighs  less  than  the  dis- 
placed liquid,  then  the  upward  force  due  to 
the  displaced  liquid  is  greater  than  its  own 
weight,  and  consequently  it  must  rise  to  the 
surface.  When  it  reaches  the  surface,  the 
downward  force  on  the  top  of  the  block,, 
due  to  the  liquid,  becomes  zero.  The  body 
must,  however,  continue 
to  rise  until  the  upward 
force  on  its  bottom  is  equal 
to  its  own  weight.  But 
this  upward  force  is  al- 


FIG.  17.  Proof  that 
a  floating  body  is 
buoyed  up  by  a 
force  equal  to  the 
weight  of  the  dis- 
placed liquid 


ways  equal  to  the  weight  of  the  displaced 
liquid,  that  is,  to  the  weight  of  the  column 
of  liquid  mbcn  (Fig.  17).  Hence 

A  floating  body  must  displace  its  own  weight 
of  the  liquid  in  which  it  floats. 

This  statement  is  embraced  in  the  state- 
ment of  Archimedes'  principle,  for  a  body 
which  floats  has  lost  its  whole  weight. 

30.  Specific  gravity  of  a  heavy  solid.  The  specific  gravity 
of  a  body  is  by  definition  the  ratio  of  its  weight  to  the  weight 
of  an  equal  volume  of  water  (§  17).  Since  a  submerged  body 
displaces  a  volume  of  water  equal  to  its  own  volume,  how- 
ever irregular  it  may  be, 

o       -a  --L       £  t,    i  Weight  of  body 

Specific  gravity  of  body  —  TTT  .  1  — ^- - 

Weight  of  water  displaced 

Making  application  of  Archimedes'  principle,  we  have 

£  i.  j  Weight  of  body 

Specific  gravity  of  body  = --» 

Loss  of  weight  in  water 

Fig.  18  shows  a  common  method  of  weighing  under  water. 


FIG.  18.   Method  of 

weighing     a     body 

under  water 


ARCHIMEDES  (287-212  B.C.) 
(Bust  in  Naples  Museum) 

The  celebrated  geometrician  of  antiquity;  lived  at  Syracuse, 
Sicily;  first  made  a  determination  of  IT  and  computed  the  area 
of  the  circle ;  discovered  the  laws  of  the  lever  and  was  author  of 
the  famous  saying,  "  Give  me  where  I  may  stand  and  I  will  move 
the  world";  discovered  the  laws  of  flotation;  invented  various 
devices  for  repelling  the  attacks  of  the  Romans  in  the  siege  of 
Syracuse ;  on  the  capture  of  the  city,  while  in  the  act  of  drawing 
geometrical  figures  in  a  dish  of  sand,  he  was  killed  by  a  Roman 
soldier  to  whom  he  cried  out,  "  Don't  spoil  my  circle  " 


THE  DETAILS  OF  A  SUBMARINE 

The  submarine,  one  of  the  newest  of  marine  inventions,  is  a  simple  application  of 
the  principle  of  Archimedes,  — one  of  the  oldest  principles  of  physics.  In  order  to 
submerge,  the  submarine  allows  water  to  enter  her  ballast  tanks  until  the  total 
weight  of  the  boat  and  contents  becomes  nearly  as  great  as  that  of  the  water  she 
is  able  to  displace.  The  boat  is  then  almost  submerged.  When  she  is  under  head- 
way in  this  condition,  a  proper  use  of  the  horizontal,  or  diving,  rudders  sends  her 
beneath  the  surface,  or,  if  submerged,  brings  her  to  the  surface,  so  that  she  can 
scan  the  horizon  with  her  periscope.  The  whole  operation  takes  but  a  few  seconds. 
When  the  submarine  wishes  to  come  to  the  surface  for  recharging  her  batteries 
or  for  other  purposes,  she  blows  compressed  air  into  her  ballast  tanks,  thus  driv- 
ing the  water  out  of  them.  Submarines  are  propelled  on  the  surface  by  Diesel  oil 
engines ;  underneath  the  surface,  by  storage  batteries  and  electric  motors 


THE  PRINCIPLE  OF  ARCHIMEDES 


23 


FIG.  19.    Method  of  finding  specific 
gravity  of  a  light  solid 


31.  Specific  gravity  of  a  solid  lighter  than  water.    If  the 

body  is  too  light  to  sink  of  itself,  we  may  still  obtain  the 

weight  of  the  equal  volume 

of  water  by  forcing  it  beneath 

the    surface    with    a    sinker. 

Thus,  suppose  u\  represents 

the  weight  on  the  right  pan 

of  the  balance  when  the  body 

is  in  air   and  the   sinker  in 

water,  as  in  Fig.  19,  while  wz 

is  the  weight  on  the  right  pan 

when  both  body  and  sinker 

are  under  water.  Then  w^—  w2 

is  obviously  the  buoyant  effect 

of  the  water  on  the  body  alone 

and  is  therefore  equal  to  the  weight  of  the  displaced  water. 

32.  Specific  gravity  of  liquids  by  the  hydrometer  method. 
The  commercial  hydrometer  such  as  is  now  in  common  use 
for  testing  the  specific  gravity  of  alcohol,  milk, 

acids,  sugar  solutions,  etc.  is  of  the  form  shown 
in  Fig.  20.  The  stem  is  calibrated  by  trial  so 
that  the  specific  gravity  of  any  liquid  may  be 
read  upon  it  directly.  The  principle  involved  is 
that  a  floating  body  sinks  until  it  displaces  its 
own  weight.  By  making  the  stem  very  slender 
the  sensitiveness  of  the  instrument  may  be  made 
very  great.  Why  ? 

33.  Specific    gravity   of    liquids    by   "loss    of 
weight "     method.      If    any    suitable     solid    be 
weighed,  first  in  air,  then  in  water,  and  then  in 
a  liquid    of   unknown   specific   gravity,   by  the 
principle  of   Archimedes  the   loss   of   weight  in 

the  liquid  is  equal  to  the  weight   of  the   liquid   displaced, 
and  the  loss  in  water  is  equal  to  the  weight  of  the  water 


FIG.  20.  Con- 
stant-weight 
hydrometer 


24 


PRESSURE  IN  LIQUIDS 


displaced.  If  we  divide  the  loss  of  weight  in  the  liquid  by 
the  loss  of  weight  in  water,  we  are  dividing  the  weight  of  a 
given  volume  of  liquid  by  the  weight  of  an  equal  volume  of 
water.  Therefore^ 

To  find  the  specific  gravity  of  a  liquid,  divide  the  loss  of 
weight  of  some  solid  in  it  by  the  loss  of  weight  of  the  same  body 
in  water.* 

QUESTIONS  AND  PROBLEMS 

1.  Let  a  vessel  of  water,  together  with  an  object  heavier  than  water, 
be  counterpoised  as  in  Fig.  21  (position  a).  Now  if  the  object  be  placed 
inside  the  vessel  of  water  (position  6),  will  the  scales  remain  balanced? 
Predict  the  result  and  then 

try  the  experiment. 

2.  Does    the    weight   ap- 
parently lost  by  a  submerged 
body  depend  upon  its  volume 
or  its  weight  ?    Explain. 

3.  A  brick  lost  1  Ib.  when 
submerged  1  ft.  deep;    how 
much   would  it  lose   if  sus- 
pended 3  ft.  deep  ? 

4.  Will  a  boat  rise  or  sink 
deeper  in  the  water  as  it  passes 
from  a  river  to  the  ocean  ? 

5.  A    fish    lies    perfectly  FIG.  21 
motionless    near   the    center 

of  an  aquarium.    What  is  the  average  density  of  the  fish?   Explain. 

6.  Where  do  the  larger  numbers  appear  on  hydrometers,  toward 
the  bottom  or  toward  the  top  of  the  stem  ?   Explain. 

7.  A  150-lb.  man  can  just  float.    What  is  his  volume? 

8.  Describe  fully  how  you  would  proceed  to  find  the  specific  gravity 
of  an  irregular  solid  heavier  than  water,  showing  in  every  case  why  you 
proceed  as  you  do. 

9.  A  body  loses  25  g.  in  water,  23  g.  in  oil,  and  20  g.  in  alcohol.  Find 
the  specific  gravity  of  the  oil  and  of  the  alcohol. 

*  Laboratory  experiments  on  the  determination  of  the  densities  of  solids 
and  liquids  should  follow  or  accompany  the  discussion  of  this  chapter.  See, 
for  example,  Experiments  7  and  8  of  the  authors'  Manual. 


THE  PRINCIPLE  OF  ARCHIMEDES  25 

10.  A  platinum  ball  weighs  330  g.  in  air,  315  g.  in  water,  and  303  g. 
in  sulphuric  acid.    Find  the  volume  of  the  ball  and  the  specific  gravity 
of  the  platinum  and  of  the  acid. 

11.  A  piece  of  paraffin  weighed  178  g.  in  air,  and  a  sinker  weighed 
30  g.  in  water.    Both  together  weighed  8  g.  in  water.    Find  the  specific 
gravity  of  the  paraffin. 

12.  A  cube  of  iron  10  cm.  on  a  side  weighs  7500  g.    What  will  it 
weigh  in  alcohol  of  density  .82  ? 

13.  What  fraction  of  the  volume  of  a  block  of  wood  will  float  above 
water  if  its  density  is  .5  ?  if  its  density  is  .6  ?  if  its  density  is  .9  ?    State 
in  general  what  fraction  of  the  volume  of  a  floating  body  is  under  water. 

14.  If  a  rectangular  iceberg  rises  100  ft.  above  water,  how  far  does 
it  extend  below  water?    (Assume  the  density  of  the  ice  to  be  .9  that 
of  sea  water.) 

15.  A  barge  30  it.  by  15  ft.  sank  4  in.  when  an  elephant  was  taken 
aboard.    What  was  the  elephant's  weight  ? 

16.  A  cubic  foot  of  stone  weighed  110  Ib.  in  water.    Find  its  specific 
gravity. 

17.  Steel  is  three  times  as  heavy  as  aluminum.   When  equal  volumes 
of  each  are  submerged  in  water,  how  do  their  apparent  losses  of  weight 
compare  ? 

18.  The  density  of  cork  is  .25  g.  per  cubic  centimeter.    What  force 
is  required  to  push  a  cubic  centimeter  of  cork  beneath  the   surface 
of  water? 

19.  A  block  of  wood  15  cm.  by  10  cm.  by  4  cm.  floats  in  water  with 
1  cm.  in  the  air.    Find  the  weight  of  the  wood  and  its  specific  gravity. 

20.  The  specific  gravity  of  milk  is  1.032.    How  is  its  specific  gravity 
affected  by  removing  part  of  the  cream  ?  by  adding  water  ?   May  these 
two  changes  be  made  so  as  not  to  alter  its  specific  gravity  at  all? 

21.  A  piece  of  sandstone  having  a  specific  gravity  of  2.6  weighs 
480  g.  in  water.    Find  its  weight  in  air. 

22.  The  density  of  stone  is  about  2.5.    If  a  boy  can  lift  120  Ib.,  how 
heavy  a  stone  can  he  lift  to  the  surface  of  a  pond  ? 

23.  The  hull  of  a  modern  battleship  is  made  almost  entirely  of  steel, 
its  walls  being  of  steel  plates  from  6  to  18  in.  thick.    Explain  how  it 
can  float. 


CHAPTER  III 


PRESSURE  IN  AIR 

BAROMETRIC  PHENOMENA 

34.  The  weight  of  air.  To  ordinary  observation  air  is  scarcely 
perceptible.  It  appears  to  have  no  weight  and  to  offer  no  resist- 
ance to  bodies  passing  through  it.  But  if  a  bulb  is  balanced  as 
in  Fig.  22,  and  then  removed  and 
filled  with  air  under  pressure  by  a 
few  strokes  of  a  bicycle  pump,  it 
will  be  found,  when  placed  on  the 
balance  again,  to  be  heavier  than  it 
was  before.  On  the  other  hand,  if 
the  bulb  is  connected  with  an  air 
pump  and  exhausted,  it  will  be 
found  to  have  lost  weight.*  Evi- 
dently, then,  air  can  be  put  into  and 
taken  out  of  a  vessel,  weighed,  and 
handled,  just  like  a  liquid  or  a  solid. 

We  are  accustomed  to  say  that  bodies  are  "as  light  as  air  "; 
yet  careful  measurement  shows  that  it  takes  but  12  cubic  feet 
of  air  to  weigh  a  pound,  so  that  a  single  large  room  contains 
more  air  than  an  ordinary  man  can  lift.  Thus,  the  air  in  a 
room  60  feet  by  30  feet  by  15  feet  weighs  more  than  .a  ton. 
The  exact  weight  of  air  at  the  freezing  temperature  and  un- 
der normal  atmospheric  conditions  is  .001298  gram  per  cubic 
centimeter,  that  is,  1.293  grams  per  liter.  A  given  volume  of 
air  therefore  weighs  y^-  as  much  as  an  equal  volume  of  water. 

*  Another  experiment  is  to  weigh  an  electric-light  bulb,  then  puncture  it 
with  a  blowpipe  and  weigh  again. 

26 


FIG.  22.   Proof  that  air 
has  weight 


BAROMETRIC  PHENOMENA 


27 


35.  Proof  that  air  exerts  pressure.  Since  air  has  weight, 
it  is  to  be  inferred  that  air,  like  a  liquid,  exerts  force  against 
any  surface  immersed  in  it.  The  following  experiments 
prove  this. 

Let  a  rubber  membrane  be  stretched  over  a  glass  vessel,  as  in  Fig.  '23. 
As  the  air  is  exhausted  from  beneath  the  membrane  the  latter  will  be 
observed  to  be  more  and  more  depressed  until  it  will  finally  burst  under 
the  pressure  of  the  air  above. 

Again,  let  a  tin  can  be  partly  filled  with  water  and  the  water  boiled. 
The  air  will  be  expelled  by  the  escaping  steam.  While  the  boiling  is 


FIG.  23.    Rubber  mem- 
brane stretched  by  weight 
of  air 


FIG.  24.    Gallon  can  crushed  by 
atmospheric  pressure 


still  going  on,  let  the  can  be  tightly  corked,  then  placed  in  a  sink  or 
tray  and  cold  water  poured  over  it.  The  steam  will  be  condensed  and 
the  weight  of  the  air  outside  will  crush  the  can  (see  Fig.  24). 

36.  Cause  of  the  rise  of  liquids  in  exhausted  tubes.    If  the 

lower  end  of  a  long  tube  be  dipped  into  water  and  the  air 
exhausted  from  the  upper  end,  water  will  rise  in  the  tube.  We 
prove  the  truth  of  this  statement  every  time  we  draw  lemonade 
through  a  straw.  The  old  Greeks  and  Romans  explained  such 
phenomena  by  saying  that  "  nature  abhors  a  vacuum,"  and 
this  explanation  was  still  in  vogue  in  Galileo's  time.  But  in 
1640  the  Duke  of  Tuscany  had  a  deep  well  dug  near  Florence, 
and  found  to  his  surprise  that  no  water  pump  which  could 
be  obtained  would  raise  the  water  higher  than  about  32  feet 
above  the  level  in  the  well.  When  he  applied  to  the  aged 


28 


PRESSURE 


AIR 


(1) 


Galileo  (see  opposite  p.  72)  for  an  explanation,  the  latter 
replied  that  evidently  "  nature's  horror  of  a  vacuum  did  not 
extend  beyond  32  feet."  It  is  quite  likely  that  Galileo  sus- 
pected that  the  pressure  of  the  air  was  responsible  for  the 
phenomenon,  for  he  had  himself  proved  before  that  air  had 
weight;  and,  furthermore,  he  at  once  devised  another  experi- 
ment to  test,  as  he  said,  the  "  power  of  a  vacuum."  He  died 
in  1642  before  the  experiment  was  performed,  but  suggested 
to  his  pupil  Torricelli  that  he  con- 
tinue the  investigation. 

37.  Torricelli's  experiment.  Tor- 
ricelli argued  that  if  water  would 
rise  32  feet,  then  mercury,  which 
is  about  13  times  as  heavy  as  water, 
ought  to  rise  but  -^  as  high.  To 
test  this  inference  he  performed, 
in  1643,  the  following  famous 
experiment : 

Let  a  tube  about  4  ft.  long,  which  is 
sealed  at  one  end,  be  completely  filled 
with  mercury,  as  in  Fig.  25,  (J),  then 
closed  with  the  thumb  and  inverted,  and 
the  bottom  immersed  in  a  dish  of  mer- 
cury, as  in  Fig.  25,  (2).  When  the  thumb 
is  removed  from  the  bottom  of  the  tube, 
the  mercury  will  fall  away  from  the 
upper  end  of  the  tube,  in  spite  of  the 

fact  that  in  so  doing  it  will  leave  a  vacuum  above  it;  and  its  upper 
surface  will,  in  fact,  stand  about  ^  of  32  ft.,  that  is,  between  29  and 
30  in.,  above  the  mercury  in  the  dish. 

Torricelli  concluded  from  this  experiment  that  the  rise 
of  liquids  in  exhausted  tubes  is  due  to  an  outside  pressure 
exerted  by  the  atmosphere  on  the  surface  of  the  liquid, 
and  not  to  any  mysterious  sucking  power  created  by  the 
vacuum  as  is  popularly  believed  even  to-day. 


FIG.  25.   Torricelli's 
experiment 


BAKOMETKIC  PHENOMENA 


29 


FIG.  26.   Barometer 
falls  when  air  pres- 
sure on  the  mercury 
surface  is  reduced 


38.  Further  decisive  tests.    An  unanswerable  argument  in 
favor  of  this  conclusion  will  be  furnished  if  the  mercury  in 
the  tube  falls  as  soon  as  the  air  is  removed  from  above  the 

surface  of  the  mercury  in  the  dish. 

To  test  this  point,  let  the  dish  and  tube  be 

placed  on  the  table  of  an  air  pump,  as  in  Fig.  26, 

the  tube  passing  through  a 

tightly  fitting  rubber  stop- 
per A  in  the  bell  jar.    As 

soon  as  the  pump  is  started 

the  mercury  in  the  tube  will, 

in  fact,  be  seen  to  fall.   As 

the  pumping  is  continued  it 

will  fall  nearer  and  nearer 

to   the    level   in    the    dish, 

although  it  will  not  usually 

reach  it,  for  the  reason  that 

an   ordinary  vacuum  pump 

is  not  capable  of  producing 

as  good  a  vacuum  as  that  which  exists  in  the 
top  of  the  tube.  As  the  air  is  allowed  to  return 
to  the  bell  jar  the  mercury  will  rise  in  the  tube  CJIil  *  mid 

to  its  former  level. 

39.  Amount  of  the  atmospheric  pressure. 
Torricelli's  experiment  shows  exactly  how 
great   the   atmospheric   pressure   is,   since 
this  pressure  is  able  to  balance  a  column 
of  mercury  of  definite  length.    As  the  pres- 
sures along  the  same  level  ac  (Fig.  27)  are 
equal,  the  downward  pressure  exerted  by 
the    atmosphere    on    the    surface    of    the 
mercury   at  c  is   equal  to  the  downward 
pressure  of  the  column  of  mercury  at  a. 

But  the  downward  pressure  at  this  point  within  the  tube  is 
equal  to  hd,  where  d  is  the  density  of  mercury  and  li  is  the 
depth  below  the  surface  b.  Since  the  average  height  of  this 


FIG.  27.    Air  column 

to  top  of  atmosphere 

balances  the  mercury 

column  ab 


30  PRESSURE  IN  AIR 

column  at  sea  level  is  found  to  be  76  centimeters,  and  since 
the  density  of  mercury  is  13.6  grams  per  cubic  centimeter,  the 
downward  pressure  inside  the  tube  at  a  is  equal  to  76  times 
13.6  grams,  or  1033.6  grams  per  square  centimeter.  Hence 
the  atmospheric  pressure  acting  on  the  surface  of  the  mercury 
at  c  is  1033.6  grams,  or,  roughly,  1  kilogram  per  square 
centimeter.  The  pressure  of  one  atmosphere  is,  then,  about 
15  pounds  per  square  inch. 

40.  Pascal's  experiment.    Pascal  thought  of  another  way 
of  testing  whether  or  not  it  were  indeed  the  weight  of  the 
outside   air   which    sustains   the   column   of   mercury   in   an 
exhausted  tube.    He  reasoned  that,  since  the  pressure  in  a 
liquid   diminishes  on  ascending  toward   the   surface,  atmos- 
pheric pressure  ought  also  to  diminish  on  passing  from  sea 
level  to  a  mountain  top.   As  there  was  no  mountain  near  Paris, 
he  carried  Torricelli's  apparatus  to  the  top  of  a  high  tower 
and  found,  indeed,  a  slight  fall  in  the  height  of  the  column 
of  mercury.    He  then  wrote  to  his  brother-in-law,  Perrier,  who 
lived  near  Puy  de  DOme,  a  mountain  in  the  south  of  France, 
and   asked   him   to    try   the   experiment   on   a   larger   scale. 
Perrier  wrote  back  that  he  was  "  ravished  with  admiration 
and  astonishment"  when  he  found  that  on  ascending  1000 
meters  the  mercury  sank  about  8  centimeters  in  the  tube. 
This   was   in    1648,    five   years   after   Torricelli's   discovery. 

At  the  present  clay  geological  parties  actually  ascertain  dif- 
ferences in  altitude  by  observing  the  change  in  the  barometric 
pressure  as  they  ascend  or  descend.  A  fall  of  1  millimeter 
in  the  barometric  height  corresponds  to  an  ascent  of  about 
12  meters. 

41.  The  barometer.     The  modern  barometer  (Fig.  28)  is 
essentially  nothing  more  nor  less  than  Torricelli's  tube.    Tak- 
ing a  barometer  reading  consists  simply  in  accurately  measur- 
ing the  height  of  the  mercury  column.   This  height  varies  from 
73  to  76.5  centimeters  in  localities  which  are  not  far  above 


BAROMETKIC  PHENOMENA 


31 


sea  level,  the  reason  being  that  disturbances  in  the  atmosphere 
affect  the  pressure  at  the  earth's  surface  in  the  same  way  in 
which  eddies  and  high  waves  in  a  tank  of  water  would  affect 
the  liquid  pressure  at  the  bottom  of  the  tank. 
The  barometer  does  not  directly  foretell 
the  weather,  but  it  has  been  found  that  a 
low  or  rapidly  falling  pressure  is  usually 
accompanied,  or  soon  followed,  by  stormy 
conditions.  Hence  the  barometer,  although 
not  an  infallible  weather  prophet,  is  never- 
theless of  considerable  assistance  in  fore- 
casting weather  conditions  some  hours 
ahead.  Further,  by  comparing  at  a  central 
station  the  telegraphic  reports  of  barometer 
readings  made  every  few  hours  at  stations 
all  over  the  country,  it  is  possible  to  deter- 
mine in  what  direction  the  atmospheric 
eddies  which  cause  barometer  changes  and 
stormy  conditions  are  traveling  and  hence 
to  forecast  the  weather  even  a  day  or  two 
in  advance. 

42.  The  first  barometers.  Torricelli  actually 
constructed  a  barometer  not  essentially  different 
from  that  shown  in  Fig.  28  and  used  it  for 
observing  changes  in  the  atmospheric  pressure; 
but  perhaps  the  most  interesting  of  the  early 
barometers  was  that  set  up  about  1650  by  Otto 
von  Guericke  of  Magdeburg  (1602-1686)  (see 
opposite  p.  32).  He  used  for  his  barometer  a 
water  column  the  top  of  which  passed  through 
the  roof  of  his  house.  A  wooden  image  which 

floated  on  the  upper  surface  of  the  water  appeared  above  the  housetop 
in  fair  weather  but  retired  from  sight  in  foul,  a  circumstance  which 
led  his  neighbors  to  charge  him  with  being  in  league  with  Satan. 

43.  The  aneroid  barometer.    Since  the  mercurial  barometer  is  some- 
what long  and  inconvenient  to  carry,  geological  and  surveying  parties 


FIG.  28.    The  Fortin 
barometer 


32  PRESSURE  IN  AIR 

commonly  use  an  instrument  called  the  aneroid  barometer.  It  consists 
essentially  of  an  air-tight  cylindrical  box  the  top  of  which  is  a  metallic 
diaphragm  which  bends  slightly  under  the  influence  of  change  in  the 
atmospheric  pressure.  This  motion  of  the  top  of  the  box  is  multiplied 
by  a  delicate  system  of  levers  and  communicated  to  a  hand  which  moves 
over  a  dial  whose  readings  are  made  to  correspond  to  the  readings  of  a 
mercury  barometer.  These  instruments  are  made  so  sensitive  as  to 


TIG.  29.    The  aneroid  barometer 

indicate  a  change  in  pressure  when  they  are  moved  no  farther  than  from 
a  table  to  the  floor.  In  the  self-recording  aneroid  barometer,  or  baro- 
graph, used  by  the  United  States  Weather  Bureau  (Fig.  29),  several  of  the 
air-tight  boxes  are  superposed  for  greater  sensitiveness,  and  the  pressures 
are  recorded  in  ink  upon  paper  wound  about  a  drum.  Clockwork  inside 
the  drum  makes  it  revolve  once  a  week.  A  somewhat  different  form  of 
the  instrument  is  used  by  aviators  to  record  altitude. 

QUESTIONS  AND  PROBLEMS 

1.  Why  does  not  the  ink  run  out  of  a  pneumatic  inkstand  like  that 
shown  in  Fig.  30  ? 

2.  If  a  tumbler  is  filled,  or  partly  filled,  with  water,  and  a  piece  of 
writing  paper  is  placed  over  the  top,  it  may  be  inverted,  as  in  Fig.  31,  . 
without  spilling  the  water.   Explain.    What  is  the  function  of  the  paper  ? 


OTTO  VON  GUERICKE  (1602-1686) 

German  physicist,  astronomer,  and  man  of  affairs ;  mayor  of  Mag- 
deburg; invented  the  air  pump  in  1650,  and  performed  many 
new  experiments  with  liquids  and  gases ;  discovered  electrostatic 
repulsion ;  constructed  the  famous  Magdeburg  hemispheres  which 
four  teams  of  horses  could  not  pull  apart  (see  p.  33) 


Water^Outlet 


THE  MERCURY-DIFFUSION  AIR  PUMP 

The  latest  development  of  the  air  pump  is  shown  in  the  accompanying  diagram. 
It  is  over  a  million  times  more  effective  than  an  air  pump  of  the  mechanical 
kind  invented  by  Von  Guericke.  The  principle  is  as  follows:  The  jet  of  water 
pouring  out  through  J^  from  an  ordinary  water  tap  T  entrains  the  air  in  the 
chamber  C  and  thus  pulls  the  pressure  in  C"  down  to  from  10  to  15  mm.  of  mer- 
cury. Next,  the  mercury  jet  ,72>  produced  by  boiling  violently  the  mercury  above 
the  electric  furnace  F,  entrains  the  air  in  the  chamber  (J"  and  thus  lowers  the 
pressure  in  this  chamber  to,  say,  .01  mm.  of  mercury.  Again,  the  stream  of  mer- 
cury vapor  pouring  out  of  </3,  under  the  influence  of  the  furnace  F',  carries  with  it 
the  molecules  of  air  coming  out  of  C'".  Finally,  the  liquid-air  trap  freezes  out  the 
mercury  vapor,  some  of  which  would  otherwise  find  its  way  through  C'"  into  the 
high-vacuum  chamber.  So  little  air  is  finally  left  in  this  high-vacuum  chamber 
that  the  pressure  there  may  be  as  low  as  a  hundred-millionth  of  a  millimeter  of 
mercury.  Pumps  of  this  sort  are  now  used  for  exhausting  audion  bulbs  and  high- 
vacuum  rectifiers,  which  are  becoming  of  very  great  commercial  value.  The  credit 
for  the  invention  of  this  form  of  pump  belongs  primarily  to  a  fellow  countryman 
of  Von  Guericke,  Professor  Gaede,  of  Freiburg,  Germany.  Improvements  of  his 
design,  however,  have  been  made  quite  independently  and  along  somewhat 
different  lines  by  several  Americans:  namely,  Irving  Langmuir  of  the  General 
Electric  Company,  Schenectady ;  O.  E.  Buckley  of  the  Western  Electric  Company, 
New  York ;  and  W.  W.  Crawford  of  the  Victor  Electric  Company,  Chicago.  The 
particular  design  shown  in  the  diagram  is  due  to  Dr.  J.  E.  Shrader  of  the 
Westinghouse  Research  Laboratory,  Pittsburgh 


COMPRESSIBILITY  OF  AIR 


33 


3.  If  a  small  quantity  of  air  should  get  into  the  space  at  the  top  of 
the  mercury  column  of  a  barometer,  how  would  it  affect  the  readings  ? 
Why? 

4.  Would  the  pressure  of  the  atmosphere  hold  mer- 
cury as  high  in  a  tube  as  large  as  your  wrist  as  in  one 
having  the  diameter  of  your  finger  ?    Explain. 

5.  Give  three  reasons  why  mercury  is  better  than 

water  for  use  in  barometers.  FlG- 

6.  Calculate  the  number  of  tons  atmospheric  force  on  the  roof  of 
an  apartment  house  50  ft.  x  100  ft.    Why  does  the  roof  not  cave  in? 

7.  Measure  the  dimensions  of  your  classroom  in 
feet  and  calculate  the  number  of  pounds  of  air  in 
the  room. 

8.  Magdeburg    hemispheres    (Fig.  32)    are    so 
called  because   they  were  invented   by  Otto  von 
Guericke,  who  was  mayor  of  Magdeburg.    When 
the  lips  of  the  hemispheres  are  placed  in  contact 
and  the  air  exhausted  from  between  them,  it  is 
found  very  difficult  to  pull  them  apart.    Why? 

9.  Von    Guericke's    original    hemispheres    are 
still  preserved  in  the  museum  at  Berlin.     Their 

interior  diameter  is  22  in.     On  the  cover  of  the  book  which  describes 

his  experiments  is  a  picture  which  represents  four  teams  of  horses  on 

each  side  of  the  hemispheres,  trying  to  separate  them.    The  experiment 

was  actually  performed  in  this  way  before 

the  German  emperor  Ferdinand  III.    If  the 

air   was    all  removed  from  the    interior    of 

the  hemispheres,  what  force  in  pounds  was 

in  fact  required  to  pull  them  apart?   (Find 

the  atmospheric  force  on   a  circle  of  11  in. 

radius.) 


FIG.  31 


FIG.  32.    Magdeburg 
hemispheres 


COMPRESSIBILITY  AND  EXPANSIBILITY  OF  AIR 

44.  Incompressibility  of  liquids.  Thus  far  we  have  found 
very  striking  resemblances  between  the  conditions  which  exist 
at  the  bottom  of  a  body  of  liquid  and  those  which  exist  at  the 
bottom  of  the  great  ocean  of  air  in  which  we  live.  We  now 
come  to  a  most  important  difference.  It  is  well  known  that 
if  2  liters  of  water  be  poured  into  a  tall  cylindrical  vessel,  the 
water  will  stand  exactly  twice  as  high  as  if  the  vessel  contained 


34  PRESSURE  IN  AIR 

but  1  liter;  or  if  10  liters  be  poured  in,  the  water  will  stand 
10  times  as  high  as  if  there  were  but  1  liter.  This  means  that 
the  lowest  liter  in  the  vessel  is  not  measurably  compressed 
by  the  weight  of  the  water  above  it. 

It  has  been  found  by  carefully  devised  experiments  that 
compressing  weights  enormously  greater  than  these  may  be 
used  without  producing  a  marked  effect ;  for  example,  when  a 
cubic  centimeter  of  water  is  subjected  to  the  stupendous  pres- 
sure of  3,000,000  grams,  its  volume  is  reduced  to  but  .90  cubic 
centimeter.  Hence  we  say  that  water,  and  liquids  generally, 
are  practically  incompressible.  Had  it  not  been  for  this  fact 
we  should  not  have  been  justified  in  taking  the  pressure  at 
any  depth  below  the  surface  of  the  sea  as  the  simple  product 
of  the  depth  by  the  density  at  the  surface. 

The  depth  bomb,  so  successful  in  the  destruction  of  sub- 
marines, is  effective  because  of  the  practical  incompressibility 
of  water.  If  the  bomb  explodes  within  a  hundred  feet  of 
the  submarine  and  is  far  enough  down  so  that  the  force  of  the 
explosion  is  not  lost  through  expansion  at  the  surface,  the 
effect  is  likely  to  be  disastrous. 

45.  Compressibility  of  air.  When  we  study  the  effects  of 
pressure  on  air,  we  find  a  wholly  different  behavior  from  that 
described  above  for  water.  It  is  very  easy  to  compress  a  body 
of  air  to  one  half,  one  fifth,  or  one  tenth  of  its  normal  volume, 
as  we  prove  every  time  we  inflate  a  pneumatic,  tire  or  cushion  of 
any  sort.  Further,  the  expansibility  of  air  (that  is,  its  tendency 
to  spring  back  to  a  larger  volume  as  soon  as  the  pressure 
is  relieved)  is  proved  every  time  a  tennis  ball  or  a  football 
bounds,  or  the  air  rushes  out  from  a  punctured  tire. 

But  it  is  not  only  air  which  has  been  crowded  into  a  pneu- 
matic cushion  by  some  sort  of  pressure  pump  which  is  in 
this  state  of  readiness  to  expand  as  soon  as  the  pressure  is 
diminished;  the  ordinary  air  of  the  room  will  expand  in  the 
same  way  if  the  pressure  to  which  it  is  subjected  is  relieved. 


COMPRESSIBILITY  OF  AIR 


Thus,  let  a  liter  beaker  with  a  sheet  of  rubber  dam  tied  tightly  over 
the  top  be  placed  under  the  receiver  of  an  air  pump.  As  soon  as  the 
pump  is  set  into  operation  the 
inside  air  will  expand  with  suffi- 
cient force  to  burst  the  rubber 
or  greatly  distend  it,  as  shown 
in  Fig.  33. 

Again,  let  two  bottles  be  ar- 
ranged as  in  Fig.  34,  one  being 


FIG.  33  FIG.  34 

Illustrations  of  the  expansibility  of  air- 


stoppered    air-tight,    while    the 

other  is  uncorked.    As  soon  as 

the   two   are   placed   under   the 

receiver  of  an  air  pump  and  the  air  exhausted,  the  water  in  A  will  pass. 

over  into  B.    When  the  air  is  readmitted  to  the  receiver,  the  water  will 

flow  back.    Explain. 

46.  Why  hollow   bodies   are  not   crushed   by  atmospheric, 
pressure.    The  preceding  experiments   show  why  the   walls 
of  hollow  bodies  are  not  crushed  in  by  the  enormous  forces 
which   the  weight   of   the   atmosphere  exerts  against  them. 
For  the  air  inside  such  bodies  presses  their  walls  out  with 
as  much  force  as  the  outside  air  presses   them  in.    In  the 
experiment  of   §  35  the  inside  air  was  removed  by  the  es- 
caping steam.    When  this  steam  was  condensed  by  the  cold 
water,  the  inside  pressure  became  very  small  and   the  out- 
side pressure  then  crushed  the  can.    In  the  experiment  shown 
in  Fig.  33  it  was  the  outside  pressure  which  was  removed 
by  the   air  pump,   and   the   pressure    of  the  inside  air  then 
burst  the  rubber. 

47.  Boyle's  law.    The  first  man  to  investigate  the  exact- 
relation  between  the  change  in  the  pressure  exerted  by  a  con- 
fined body  of  gas  and  its  change  in  volume  was  an  Irishman, 
Robert  Boyle  (1627-1691).   We  shall  repeat  a  modified  form 
of  his  experiment  much  more  carefully  in  the  laboratory,  but 
the  following  will  illustrate  the  method  by  which  he  discov- 
ered one  of  the  most  important  laws  of  physics,  a  law  which 
is  now  known  by  his  name. 


36 


PRESSURE 


AIR 


Let  mercury  be  poured  into  a  bent  glass  tube  until  it  stands  at  the 
same  level,  in  the  closed  arm  A  C  as  in  the  open  arm  ED  (Fig.  35). 
There  is  now  confined  in  A  C  a  certain  volume  of  air  under  the  pressure 
of  one  atmosphere.  Call  this  pressure  Pr  Let  the  length  A  C  be  meas- 
ured and  called  Vr  Then  let  mercury  be  poured  into  the  long  arm 
until  the  level  in  this  arm  is  as  many  centimeters 
above  the  level  in  the  short  arm  as  there  are  centi- 
meters in  the  barometer  height.  The  confined  air 
is  now  under  a  pressure  of  two  atmospheres.  Call  it 
P2.  Let  the  new  volume  A^C(=  F2)  be  measured. 
It  will  be  found  to  be  just  half  its  former  value. 

Hence  we  learn  that  doubling  the  pressure 
exerted  upon  a  body  of  gas  halves  its  volume. 
If  we  had  tripled  the  pressure,  we  should  have 
found  the  volume  reduced  to  one  third  its 
initial  value,  etc.  That  is,  the  pressure  which 
a  given  quantity  of  gas  at  constant  temperature 
exerts  against  the  walls  of  the  containing  vessel 
is  inversely  proportional  to  the  volume  occupied. 
This  is  algebraically  stated  thus: 


or 


FIG.  35.    Method 

of  demonstrating 

Boyle's  law 

(i) 


This  is  Boyle's  law.  It  may  also  be  stated  in  slightly 
different  form.  Doubling,  tripling,  or  quadrupling  the  pres- 
sure must  double,  triple,  or  quadruple  the  density,  since  the 
volume  is  made  only  one  half,  one  third,  or  one  fourth  as 
much,  while  the  mass  remains  unchanged.  Hence  the  pres- 
sure which  a  gas  exerts  is  directly  proportional  to  its  density, 
or,  algebraically,  # 

&sad=4.  (<r\ 

^      D* 

48.  Extent  and  character  of  the  earth's  atmosphere.  From 
the  facts  of  compressibility  and  expansibility  of  air  we  may 

*  A  laboratory  experiment  on  Boyle's  law  should  follow  this  discussion. 
See,  for  example,  Experiment  9  of  the  authors'  Manual. 


COMPKESSIBILITY  OF  AIR 


37 


know  that  the  air,  unlike  the  sea,  must  become  less  and  less 
dense  as  we  ascend  from  the  bottom  toward  the  top.  Thus, 
at  the  top  of  Mont  Blanc,  an  altitude  of  about  three  miles, 
where  the  barometer  height  is  but  38  centimeters,  or  one  half 
of  its  value  at  sea  level,  the  density  also  must,  by  Boyle's 
law,  be  just  one  half  as  much  as  at  sea  level. 


Heights 

in  miles 


Barometer 
keif/his  in 


Air 

densities 


FIG.  36.    Extent  and  character  of  atmosphere 

No  one  has  ever  ascended  higher  than  7  miles,  which  was 
approximately  the  height  attained  in  1862  by  the  two  daring 
English  aeronauts  Glaisher  and  Cox  we  11.  At  this  altitude  the 
barometric  height  is  but  about  7  inches,  and  the  temperature 
about  —  60°  F.  Both  aeronauts  lost  the  use  of  their  limbs, 
and  Mr.  Glaisher  became  unconscious.  Mr.  Coxwell  barely 
succeeded  in  grasping  with  his  teeth  the  rope  which  opened  a 
valve  and  caused  the  balloon  to  descend.  Again,  on  July  31, 
1901,  the  French  aeronaut  M.  Berson  rose  without  injury  to 


38  PKESSUEE  IN  AIR 

a  height  of  about  7  miles  (35,420  feet),  his  success  being 
due  to  the  artificial  inhalation  of  oxygen.  The  American 
aviator  Lieutenant  John  A.  Macready  of  the  United  States 
Army,  on  September  28,  1921,  ascended  in  an  airplane  to  a 
height  of  34,563  feet.  He  found  the  temperature  —  58°  F. 

By  sending  up  self-registering  thermometers  and  barome- 
ters in  balloons  which  burst  at  great  altitudes,  the  instruments 
being  protected  by  parachutes  from  the  dangers  of  rapid  fall, 
the  atmosphere  has  been  explored  to  a  height  of  35,080 
meters  (21.8  miles),  this  being  the  height  attained  on  Decem- 
ber 7,  1911,  by  a  little  balloon  which  was  sent  up  at  Pavia, 
Italy.  These  extreme  heights  are  calculated  from  the  indi- 
cations of  the  self -registering  barometers. 

At  a  height  of  35  miles  the  density  of  the  atmosphere  is 
estimated  to  be  but  30Q00  of  its  value  at  sea  level.  By  calcu- 
lating how  far  below  the  horizon  the  sun  must  be  when  the 
last  traces  of  color  disappear  from  the  sky,  we  find  that  at  a 
height  as  great  as  45  miles  there  must  be  air  enough  to  reflect 
some  light.  How  far  beyond  this  an  extremely  rarified  atmos- 
phere may  extend,  no  one  knows.  It  has  been  estimated  at 
all  the  way  from  100  to  500  miles.  These  estimates  are  based 
on  observations  of  the  height  at  which  meteors  first  become 
visible,  on  the  height  of  the  aurora  borealis,  and  on  the  dark- 
ening of  the  surface  of  the  moon  just  before  it  is  eclipsed  by 
the  shadow  of  the  solid  earth. 

QUESTIONS  AND  PROBLEMS 

1.  The   deepest   sounding  in  the   ocean  is   about  6  mi.    Find  the 
pressure  in  tons  per  square  inch  at  this  depth.     (Specific   gravity  of 
ocean    water  =  1.026.)     Will    a   pebble    thrown    overboard   reach    the 
bottom  ?    Explain. 

2.  What  sort  of  a  change  in  volume  do  the  bubbles  of  air  which 
escape  from  a  diver's  suit  experience  as  they  ascend  to  the  surface  ? 

3.  With  the  aid  of  the  experiment  in  which  the  rubber  dam  was 
burst  under  the  exhausted  receiver  of  an  air  pump  explain  why  high 


COMPRESSIBILITY  OF  AIE 


39 


mountain  climbing  ofieii  causes  pain  and  bleeding  in  the  ears  and  nose. 
Why  does  deep  diving  produce  similar  effects? 

4.  Blow  as  hard  as  possible  into  the  tube  of  the  bottle  shown  in 
Fig.  37.    Then  withdraw  the    mouth  and  explain  all  of  the    effects 
observed. 

5.  If  a  bottle  or  cylinder  is  filled  with  water  and  inverted  in  a  dish 
of  water,  with  its  mouth  beneath  the  surface  (see  Fig.  38),  the  water 
will  not  run  out.    Why  ? 

6.  If  a  bent  rubber  tube  is  inserted  beneath  the  cylinder 
and  air  blown  in  at  o  (Fig.  38),  it  will  rise  to  the  top  and 
displace  the  water.    This  is  the  method  regularly  used  in  col- 
lecting gases.     Explain  what  forces  the  gas  up  into  it,  and 
what  causes  the  water  to  descend  in  the  tube  as  the  gas  rises. 

7.  Why  must  the  bung  be  removed  from  a  cider  barrel  in 
order  to  secure  a  proper  flow  from  the  faucet  ? 

8.  When  a  bottle  full  of  water  is  inverted,  the  water  will     FIG.  37 
gurgle  out  instead  of  issuing  in  a  steady  stream.    Why? 

9.  If  100  cu.  ft.  of  hydrogen  gas  at  normal  pressure  are  forced  into 
a  steel  tank  having  a  capacity  of  5  cu.  ft.,  what  is  the  gas  pressure  in 
pounds  per  square  inch  ? 

10.  An  automobile  tire  having  a  capacity  of  1500  cu.  in.  is  inflated 
to  a  pressure  of  90  pounds  per  square  inch.    What  is  the  density  of  the 
air  within  the  tire?    To  what  volume  would  the  air 

expand  if  there  should  be  a  "  blow-out "  ? 

11.  Under  ordinary  conditions  a  gram  of  air  occu- 
pies about  800  cc.  Find  what  volume  a  gram  will  occupy 
at  the  top  of  Mont  Blanc  (altitude  15,781  ft.),  where  the 
barometer  indicates  that  the  pressure  is  only  about  one 
half  what  it  is  at  sea  level. 

12.  The  mean  density  of  the  air  at  sea  level  is  about 

.0012.    What  is  its  density  at  the  top  of  Mont  Blanc?          FIG.  38. 

What  fractional   part  of  the  earth's    atmosphere  has 

one  left  beneath  him  when  he  ascends  to  the  top  of  this  mountain  ?' 

13.  If  Glaisher  and  Coxwell  rose  in  their  balloon  until  the  barometric 
height  was  only  18  cm.,  how  many  inhalations  were  they  obliged  to- 
il lake  in  order  to  obtain  the  same  amount  of  air  which  they  could 
obtain  at  the  surface  in  one  inhalation  ? 

14.  1  cc.    of   air   at  the   earth's   surface    weighs    .00129  g.    If    this, 
were  the   density   all  the  way  up,  to  what  height   would  the   atmos- 
phere extend? 


40 


PRESSURE  IX  AIR 


PNEUMATIC  APPLIANCES 

49.    The  siphon.    Let  a  rubber  or  glass  tube  be  filled  with  water  and 
then  placed  in  the  position  shown  in  Fig.  39.   Water  will  be  found  to 
flow  through  the  tube  from  vessel  A  into  vessel  B.    If  then  B  be  raised 
until  the  water  in  it  is  at  a  higher  level  than 
that  in  A,  the  direction  of  flow  will  be  reversed. 
This  instrument,  which  is  called  the  siphon,  is 
very   useful  for   removing    liquids  from  vessels 
which  cannot  be  overturned,  or  for  drawing  off 
the  upper  layers  of  a  liquid  without  disturbing 
the  lower  layers.    Many  commercial  applications 
of  it  are  found  in  various  siphon  flushing  systems. 


f  1 


i 


The  explanation  of  the  siphon's  action  pIG.  39.  The  siphon 
is  readily  seen  from  Fig.  39.  Since  the 
tube  acb  is  full  of  water,  water  must  evidently  flow  through 
it  if  the  force  which  pushes  it  one  way  is  greater  than  that 
which  pushes  it  the  other  way.  Now  the  upward  pressure  at 
a  is  equal  to  atmospheric  pressure  minus  the  downward  pres- 
sure due  to  the  water  column  ad,  while  the  upward  pres- 
sure at  b  is  the  atmospheric  pressure  minus  the  downward 
pressure  due  to  the  water  column  be. 
Hence  the  pressure  at  a  exceeds  the  pres- 
sure at  b  by  the  pressure  due  to  the  water 
column  fb.  The  siphon  will  evidently 
cease  to  act  when  the  water  is  at  the  same 
level  in  the  two  vessels,  since  then/5  =  0 
and  the  forces  acting  at  the  two  ends  of 
the  tube  are  therefore  equal  and  opposite. 
It  will  also  cease  to  act  when  the  bend  c 
is  more  than  34  feet  above  the  surface  of  the  water  in  A, 
since  then  a  vacuum  will  form  at  the  top,  atmospheric 
pressure  being  unable  to  raise  water  to  a  height  greater  than 
this  in  either  tube. 

Would  a  siphon  flow  in  a  vacuum  ? 


FIG.  40.  Intermittent 
siphon 


PNEUMATIC  APPLIANCES 


41 


50.  The  intermittent  siphon.     Fig.  40    represents    an   intermittent 
siphon.    If  the  vessel  is  at  first  empty,  to  what  level  must  it  be  filled 
before  the  water  will  flow  out  at  o  ?  To  what  level  will  the  water  then 
fall  before  the  flow  will  cease  ? 

51.  The  air  pump.    The  air  pump  was  invented  in  1650 
by  Otto  von  Guericke,  mayor  of  Magdeburg,  Germany,  who 

deserves  the  greater  credit  since  he 
was  apparently  altogether  without 
knowledge  of  the  discoveries  which 
Galileo,  Torricelli,  and  Pascal  had 
made  a  few 
years  earlier 
regarding  the 
character  of  the 
earth's  atmos- 


FIG. 41.    A  simple  air  pump 


phere.  A  simple  form  of  such  a  pump 
is  shown  in  Fig.  41.  When  the  piston 
is  raised,  the  air  from  the  receiver  R 
expands  into  the  cylinder  B  through  the 
valve  A.  When  the  piston  descends,  it 
compresses  this  air  and  thus  closes 
the  valve  A  and  opens  the  exhaust 
valve  C.  Thus,  with  each  double  stroke 
a  certain  fraction  of  the  air  in  the 
receiver  is  transferred  from  R  through 
the  cylinder  to  the  outside. 

In  many  pumps  the  valve  C  is  in  the 
piston  itself. 

52.  The  compression  pump.    A  com- 
pression pump  is  used  for  compressing 

a  gas  into  a  container.  If  the  pump  shown  in  Fig.  41  be 
detached  from  the  receiver  plate  and  the  vessel  to  receive 
the  gas  be  attached  at  (7,  we  have  a  compression  pump. 
Fig.  42  shows  a  common  form  of  compression  pump  used  for 


FIG.  42.   Automobile 
compression  pump 


PRESSURE  IK  AIR 


inflating  automobile  tires.  Cup  valves  are  shown  at  c  and  <?'. 
They  are  leather  disks  a  little  larger  than  the  barrel  of  the 
pump,  attached  to  a  loosely  fitting  metal  piston. 

When  the  pistons  are  forced  down,  the  valve  c  spreads 
tightly  against  the  wall,  forcing  the  air  past  the  valves  c 
and  v.  On  the  upstroke  the  valve  c'  spreads  and  forces  the 
compressed  air  in  the  small  barrel  past  v,  while  at  the  same 
time  air  passes  by  c,  again  filling  the  two  barrels,  v  prevents 
any  air  from  reentering  the  small  barrel  from  the  hose  h. 
The  greater  compressing  power  of  the  two-barreled  pump 
is  due  to  the  fact  that  cf  on  the  upstroke  compresses  air  that 
has  already  been  compressed  by  c  on  the 
downstroke. 

Compressed  air  finds  so  many  applications 
in  such  machines  as  air  drills  (used  in  min- 
ing), air  brakes,  air  motors,  etc.  that  the 
compression  pump  must  be  looked  upon  as 
of  much  greater  importance  industrially  than 
the  exhaust  pump. 

53.  The  lift  pump.  The  common  water 
pump,  shown  in  Fig.  43,  has  been  in  use  at 
least  since  the  time  of  Aristotle  (fourth  cen- 
tury B.  c.).  It  will  be  seen  from  the  figure 
that  it  is  nothing  more  nor  less  than  a 
simplified  form  of  air  pump.  In  fact,  in  the  earlier  strokes 
we  are  simply  exhausting  air  from  the  pipe  below  the  valve  b. 
Water  could  never  be  obtained  at  S,  even  with  a  perfect 
pump,  if  the  valve  b  were  not  within  34  feet  of  the  surface 
of  the  water  in  W.  Why  ?  On  account  of  mechanical  im- 
perfections this  limit  is  usually  about  28  feet  instead  of  34. 
Let  the  student  analyze,  stroke  by  stroke,  the  operation  of 
pumping  water  from  a  well  with  the  pump  of  Fig.  43.  Why 
will  pouring  in  a  little  water  at  the  top,  that  is,  "  priming," 
often  assist  greatly  in  starting  such  a  pump  ? 


FIG.  43.   The  lift 
pump 


PNEUMATIC  APPLIANCES 


54.  The  force  pump.    Fig.  44  illustrates  the  construction  of 
the  force  pump,  a  device  commonly  used  whe;i  it  is  desired 
to  deliver  water  at  a  point  higher  than  the  position  at  which 
it  is  convenient  to   place    the  pump 

itself.  Let  the  student  analyze  the 
action  of  the  pump  from  a  study  of 
the  diagram. 

In  order  to  make  the  flow  of  water 
in  the  pipe  HS  continue  during  the 
upstroke,  an  air  chamber  is  always 
inserted  between  the  valve  a  and  the 
discharge  point.  As  the  water  is 
forced  violently  into  this  chamber  by 
the  downward  motion  of  the  piston 
it  compresses  the  confined  air.  It  is, 
then,  the  reaction  of  this  compressed 
air  which  is  immediately  responsible  for  the  flow  in  the  dis- 
charge tube ;  and  as  this  reaction  is  continuous,  the  flow  is 
also  continuous. 

55.  The   Cartesian   diver.     Descartes 
(1596-1650),  the  great  French  philoso- 
pher, invented  an  odd  device  which  illus- 
trates at  the  same  time  the  principle  of 
the  transmission  of  pressure  by  liquids, 
the   principle   of   Archimedes,   and  the 
compressibility  of  gases.   A  hollow  glass 
image  in  human  shape   (Fig.  45,  (1)) 
has  an  opening  in  the  lower  end.    It  is 
filled  partly  with  water  and  partly  with 

air,  so  that  it  will  just  float.  By  pressing  on  the  rubber  dia- 
phragm at  the  top  of  the  vessel  it  may  be  made  to  sink  or 
rise  at  will.  Explain.  If  the  diver  is  not  available,  a  small 
bottle  or  test  tube  (Fig.  45,  (2))  may  be  used  instead ;  it 
works  equally  well  and  brings  out  the  principle  even  better. 


FIG.  44.   The  force  pump 


(2) 


FIG.  45. 


The  Cartesian 
diver 


44 


PRESSURE  IN  AIR 


The  modern  submarine  (see  opposite  page  23)  is  essentially 
nothing  but  a. huge  Cartesian  diver  which  is  propelled  above 
water  by  oil  or  steam  engines,  and  when  submerged,  by  electric 
motors  driven  by  storage  batteries.  The  volume  of  the  air  in 
its  chambers  is  changed  by  forcing  water  in  or  out,  and  it  dives 
by  a  combined  use  of  the  propeller  and  horizontal  rudders. 

56.  The  balloon.  A  reference  to  the  proof  of  Archimedes'  principle 
(§  29,  p.  21)  will  show  that  it  must  apply  as  well  to  gases  as  to  liquids. 
Hence  any  body  immersed  in  air  is  buoyed  up  l>y  a  force  which  is  equal 
to  the  weight  of  the  displaced  air.  The  body 
will  therefore  rise  if  its  own  weight  is  less 
than  the  weight  of  the  air  which  it  displaces. 

A  balloon  is  a  large  silk  bag  (see  opposite 
page  45)  impregnated  with  rubber  and  filled 
either  with  hydrogen  or  with  common  illumi- 
nating gas.  The  former  gas  weighs  about  .09 
kilogram  per  cubic  meter,  and  common  illumi- 
nating gas  weighs  about  .75  kilogram  per  cubic 
meter.  It  will  be  remembered  that  ordinary  air 
weighs  about  1.20  kilograms  per  cubic  meter. 
It  will  be  seen,  therefore,  that  the  lifting  force 
of  hydrogen  per  cubic  meter  namely,  1.20  — 
.09  =  1.11,  is  more  than  twice  the  lifting  force 
of  illuminating  gas,  1.20  —  .75  =  .45. 

Ordinarily  a  balloon  is  not  completely  filled 

at  the  start ;  for  if  it  were,  since  the  outside  pressure  is  continually 
diminishing  as  it  ascends,  the  pressure  of  the  inside  gas  would  subject 
the  bag  to  enormous  strain  and  would  surely  burst  it  before  it  reached 
any  considerable  altitude.  But  if  it  is  but  partially  inflated  at  the  start, 
it  can  increase  in  volume  as  it  ascends  by  simply  inflating  to  a  greater 
extent.  Thus,  a  balloon  which  ascends  until  the  pressure  is  but  7  centi- 
meters of  mercury  should  be  only  about  one  fourth  inflated  when  it  is 
at  the  surface. 

The  parachute  (Fig.  46)  is  a  huge,  umbrella-like  affair  with  which 
the  aeronaut  may  descend  in  safety  to  the  earth.  After  opening,  it 
descends  very  slowly  on  account  of  the  enormous  surface  exposed  to  the 
air.  A  hole  in  the  top  allows  air  to  escape  slowly,  and  thus  keeps  the 
parachute  upright. 


FIG.  40.   The  parachute 


PNEUMATIC  APPLIANCES 


45 


57.  Helium  balloons.    One  of  the  striking  results  of  the  World  War 
was  the  development  of  the  helium  balloon.    Helium  is  a  noninflam- 
mable  gas  twice  as  dense  as  hydrogen  and  having  a  lifting  power  .92  as 
great.    It  is  so  rare  an  element  that  before  the  war  not  over  100  cu.  ft. 
had  been  collected  by  anyone.    Its  pre-war  price  was  $1700  per  cu.  ft. 
At  the  close  of  the  war  147,000  cu.  ft.,  extracted  at  a  cost  of  ten  cents 
a  cubic   foot  from  the   gas  wells  of  Texas  and  Okla- 
homa, were  ready  for  shipment  to  France,  and  plans 

were  under  way  for  producing  it  at  the  rate  of  50,000 
cu.  ft.  per  day.  The  production  of  a  balloon  gas  that 
assures  safety  from  fire  opens  up  a  new  era  for  the 
dirigible  balloon  (see  opposite  page  44). 

58.  The  diving  bell.  The  diving  bell  (Fig.  47) 
is  a  heavy,  bell-shaped  body  with  rigid  walls, 

which  sinks  of  its  own  weight.  Formerly  the  workmen  who 
went  down  in  the  bell  had  at  their  disposal  only  the  amount  of 
air  confined  within  it,  and 
the  water  rose  to  a  certain 
height  within  the  bell  on 
account  of  the  compression 
of  the  air.  But  in  modern 
practice  the  air  is  forced  in 
from  the  surface  through  a 
connecting  tube  a  (Fig.  48) 
by  means  of  a  force  pump  h. 
This  arrangement,  in  addi- 
tion to  furnishing  a  con- 
tinual supply  of  fresh  air, 
makes  it  possible  to  force 
the  water  down  to  the 

level  of  the  bottom  of  the 

i    n      T  ,.  . .  FIG.  48.    Laying  foundations  of  piers 

bell.    In  practice  a  contm-  with  the  diving  bell 

ual   stream   of    bubbles    is 

kept  flowing  out  from  the  lower  edge  .of  the  bell,  as  shown 

in  Fig.  48,  which  illustrates  subaqueous  construction. 


46 


PRESSURE  IN  AIR, 


The  pressure  of  the  air  within  the  bell  must,  of  course,  be 
the  pressure  existing  within  the  water  at  the  depth  of  the 
level  of  the  water  inside  the  bell;  that  is,  in  Fig.  47  at  the 
depth  AC.  Thus,  at  a  depth  of  34  feet  the  pressure  is  2 
atmospheres.  Diving  bells  are  used  for  putting  in  the  founda- 
tions of  bridge  piers,  doing  subaqueous  excavating,  etc.  The 
so-called  caisson,  much  used  in  bridge  building,  is  simply  a 
huge  stationary  diving  bell,  which  the  workmen  enter  through 
compartments  provided  with  air-tight  doors.  Air  is  pumped 
into  it  precisely  as  in  Fig.  48. 

59.  The  diving  suit.     For  most  purposes  except  those  of  heavy  engi- 
neering the  diving  suit  (Fig.  49)  has  now  replaced  the  diving  bell.    This 
suit  is  made  of  rubber  and  has  a  metal  helmet.   The  diver  is  sometimes 
connected  with  the  surface  by  a  tube  through  which 

air  is  forced  down  to  him.  It  passes  out  into  the 
water  through  the  valve  V  in  his  suit.  But  more 
commonly  the  diver  is  entirely  independent  of  the 
surface,  carrying  air  under  a  pressure  of  about  40  at- 
mospheres in  a  tank  on  his  back.  This  air  is  allowed 
to  escape  gradually  through  the  suit  and  out  into  the 
water  through  the  valve  V  as  fast  as  the  diver  needs 
it.  When  he  wishes  to  rise  to  the  surface,  he  simply 
admits  enough  air  to  his  suit  to  make  him  float. 

In  all  cases  the  diver  is  subjected  to  the  pressure  ex- 
isting at  the  depth  at  which  the  suit  or  bell  commu- 
nicates with  the  outside  water.  Divers  seldom  work 
at  depths  greater  than  60  feet,  and  80  feet  is  usually 
considered  the  limit  of  safety.  But  Chief  Gunner's 
Mate  Frank  Crilley,  investigating  the  sunken  U.  S. 
submarine  f-4  at  Honolulu  in  1915,  descended  to  a 
depth  of  304  feet. 

The  diver  experiences  pain  in  the  ears  and  above 

the  eyes  when  he  is  ascending  or  descending,  but  not  when  at  rest.  This 
is  because  it  requires  some  time  for  the  air  to  penetrate  into  the  interior 
cavities  of  the  body  and  establish  equal  pressure  in  both  directions. 

60.  The  gas  meter.   Gas  from  tjie  city  supply  enters  the  meter  through 
P  (Fig.  50)  and  passes  through  the  openings  o  and  ox  into  the  compart- 
ments B  and  Bl  of  the  meter.   Here  its  pressure  forces  in  the  diaphragms 


FIG.  49.   The  div- 
ing suit 


PNEUMATIC  APPLIANCES 


47 


d  and  dr  The  gas  already  contained  in  A  and  A1  is  therefore  pushed 
out  to  the  burners  through  the  openings  of  and  o^  and  the  pipe  Pr  As 
soon  as  the  diaphragm  d  has  moved  as  far  as  it  can  to  the  right,  a  lever 
which  is  worked  by  the  movement  of  d  causes  the  slide  valve  u  to  move 
to  the  left,  thus  closing  o  and  shutting  off  con- 
nection between  P  and  B,  but  at  the  same  time 
opening  o'  and  allowing  the  gas  from  P  to  enter 
compartment  A  through  o'.  A  quarter  of  a  cycle 
later  u^  moves  to  the  right  and  connects  Al 
with  P  and  Bl  with  Pr  If  u  and  u^  were  set 
so  as  to  work  exactly  together,  there  would 
fye  slight  fluctuations  in  the  gas  pressure  at  Pr 
The  movement  of  the  diaphragms  is  recorded 
by  a  clockwork  device,  the  dials  of  which  in- 
dicate the  number  of  cubic  feet  of  gas  which 
have  passed  through  the  meter.  FIG.  50.  The  gas  meter 


QUESTIONS  AND  PROBLEMS 

1.  A  water  tank  8  ft.  deep,  standing  some  distance  above  the  ground, 
closed  everywhere  except  at  the  top,  is  to  be  emptied.    The  only  means 
of  emptying  it  is  a  flexible  tube,    (a)  What  is  the  most  convenient  way 
of  using  the  tube,  and  how  could  it  be  set  into  operation  ?    (b)  How 
long  must  the  tube  be  to  empty  the  tan.fc  completely? 

2.  Kerosene  has  a  specific  gravity  of  .8.    Over  what  height  can  it  be 
siphoned  at  normal  pressure  ? 

3.  Let  a  siphon  of  the  form  shown  in  Fig.  51  be  made  by  filling  a 
flask  one  third  full  of  water,  closing  it  with  a  cork  through 

which  pass  two  pieces  of  glass  tubing,  as  in  the  figure, 
and  then  inverting  so  that  the  lower  end  of  the  straight 
tube  is  in  a  dish  of  water.  If  the  bent  arm  is  of  consid- 
erable length,  the  fountain  will  play  forcibly  and  continu- 
ously until  the  dish  is  emptied.  Explain. 

4.  Diagram   a   lift  pump  on  upstroke.    What  causes 
the  water  to  rise  in  the  suction  pipe  ?    What  happens  on 
downstroke  ? 

5.  Diagram   a  force  pump  with  air  dome   on  down- 
stroke.    What  happens  on  upstroke  ?  FIG.  51 

6.  If  the  cylinder    of   an   air    pump  is   of  the   same 

size  as  the  receiver,  what  fractional  part  of  the  air  is  removed  by 
one  complete  stroke?  What  fractional  part  is  left  after  3  strokes? 
after  10  strokes  ? 


48 


PRESSURE  IN  AIR 


CUBIC 


FEET 


CUBIC 


FEET 


7.  If  the  cylinder  of  an  air  pump  is  one  third  the  size  of  the  receiver, 
what  fractional  part  of  the  original  air  will  be  left  after  5  strokes? 
What  will  be  the  reading  of  a  barometer  within  the  receiver,  the  outside 
pressure  being  76  ? 

8.  Theoretically,  can  a  vessel  ever  be  completely  exhausted  by  an 
air  pump,  even  if  mechanically  perfect  ? 

9.  Explain  by  reference  to  atmospheric  pressure  why  a  balloon  rises. 

10.  How  many  of  the  laws  of  liquids  and  gases  do  you  find  illustrated 
in  the  experiment  of  the  Cartesian 

diver? 

11.  Pneumatic    dispatch    tubes 
are  now  used  in  many  large  stores 
for  the  transmission  of  small  pack- 
ages. An  exhaust  pump  is  attached 
to  one  end  of  the  tube  in  which  a 
tightly  fitting  carriage  moves,  and 
a  compression  pump  to  the  other. 
If  the  air  is  half  exhausted  on  one 
side  of  the  carriage  and  has  twice 
its    normal   density  on  the    other, 
find  the  propelling  force  acting  on 
the  carriage  when  the  area  of  its 
cross  section  is  50  sq.  cm. 

12.  What  determines  how  far  a 
balloon  will  ascend?    Under  what 
conditions  will  it  begin  to  descend  ? 
Explain  these  phenomena  by  the 
principle  of  Archimedes. 

13.  If  a  diving  bell  (Fig.  47)  is  sunk  until  the  level  of  the  water  within 
it  is  1033  cm.  beneath  the  surface,  to  what  fraction  of  its  initial  volume 
has  the  inclosed  air  been  reduced  ?   (1033  g.  per  sq.  cm.  =  1  atmosphere.) 

14.  If  a  diver's  tank  has  a  volume  of  2  cu.  ft.  and  contains  air  under 
a  pressure  of  40  atmospheres,  to  what  volume  will  the  air  expand  when 
it  is  released  at  a  depth  of  34  ft.  under  water  ? 

15.  A  submarine  weighs  1800  tons  when  its  submerging  tanks  are 
empty,  and  in  that  condition  10  per  cent  by  volume  of  the  submarine 
is  above  water.    What  weight  of  water  must  be  let  into  the  tanks  to 
just  submerge  the  boat? 

16.  (a)  The  upper  figure  shows  a  reading  of  84,600  cu.  ft.  of  gas. 
The  lower  figure  shows  the  reading  of  the  meter  a  month  later.    What 
was  the  amount  of  the  bill  for  the  month  at  $.80  per  1000  cu.  ft.  ? 
(b)  Diagram  the  meter  dials  to  represent  49,200  cu.  ft. 


FIG.  52.    The  dials  of  a  gas  meter 


CHAPTER  IV 

MOLECULAR  MOTIONS 
KINETIC  THEORY  OF  GASES 

61.  Molecular  constitution  of  matter.    In  order  to  account 
for  some  of  the  simplest  facts  in  nature  —  for  example,  the 
fact  that  two  substances  often  apparently  occupy  the  same 
space  at  the  same  time,  as  when  two  gases  are  crowded  together 
in  the  same  vessel  or  when  sugar  is  dissolved  in  water  —  it 
is  now  universally  assumed  that  all  substances  are  composed 
of  very  minute  particles  called  molecules.  Spaces  are  supposed 
to  exist  between  these  molecules,  so  that  when  one  gas  enters 
a  vessel  which  is  already  full  of  another  gas  the  molecules 
of  the  one  scatter  themselves  about  among  the  molecules  of 
the  other.     Since  molecules  cannot  be  seen  with  the  most 
powerful  microscopes,  it  is  evident  that  they  must  be  very 
minute.     The  number  of  them  contained  in  a  cubic  centi- 
meter of  air  is  27  billion  billion  (27  x  1018).    It  would  take 
as  many  as  a  thousand  molecules  laid  side  by  side  to  make 
a  speck  long  enough  to  be  seen  with  the  best  microscopes. 

62.  Evidence  for  molecular  motions  in  gases.    Certain  very 
simple  observations  lead  us  to  the  conclusion  that  the  mole- 
cules of  gases,  even  in  a  still  room,  must  be  in  continual  and 
quite  rapid  motion.     Thus,  if  a  little  chlorine,  or  ammonia, 
or  any  gas  of  powerful  odor  is  introduced  into  a  room,  in  a 
very  short  time  it  will  have  become  perceptible  in  all  parts  of 
the  room.    This  shows  clearly  that  enough  of  the  molecules 
of  the  gas  to  affect  the  olfactory  nerves  must  have  found 
their  way  across  the  room. 

49 


50 


MOLECULAR  MOTIONS 


FIG.  53.    Illustrat- 
ing   the    diffusion 
of  gases 


Again,  chemists  tell  us  that  if  two  globes,  one  containing 
hydrogen  and  the  other  carbon  dioxide  gas,  be  connected  as 
in  Fig.  53,  and  the  stopcock  between  them  opened,  after  a 
few  hours  chemical  analysis  will  show  that  each  of  the  globes 
contains  the  two  gases  in  exactly  the  same 
proportions,  —  a  result  which  is  at  first  sight 
very  surprising,  since  carbon  dioxide  gas  is 
about  twenty-two  times  as  heavy  as  hydrogen. 
This  mixing  of  gases  in  apparent  violation  of 
the  laws  of  weight  is  called  diffusion. 

We  see,  then,  that  such  simple  facts  as 
the  transference  of  odors  and  the  diffusion 
of  gases  furnish  very  convincing  evidence 
that  the  molecules  of  a  gas  are  not  at  rest 
but  are  continually  moving  about. 

63.  Molecular  motions  and  the  indefinite 
expansibility  of  a  gas.     Perhaps  the  most 

striking  property  which  we  have  found  gases  to  possess  is  the 
property  of  indefinite  or  unlimited  expansibility.  The  exist- 
ence of  this  property  was  demonstrated  by  the  fact  that  we 
were  able  to  attain  a  high  degree  of  exhaustion  by  means  of 
an  air  pump.  No  matter  how  much  air  was  removed  from  the 
bell  jar,  the  remainder  at  once  expanded  and  filled  the  entire 
vessel.  The  motions  of  the  molecules  furnish  a  thoroughly 
satisfactory  explanation  of  the  phenomenon. 

The  fact  that,  however  rapidly  the  piston  of  the  air  pump 
is  drawn  up,  gas  always  appears  to  follow  it  instantly,  leads 
us  to  the  conclusion  that  the  natural  velocity  possessed  by 
the  molecules  of  gas  must  be  very  great. 

64.  Molecular  motions  and  gas  pressures.    How  are  we  to 
account  for  the  fact  that  gases  exert  such  pressures  as  they 
do   against   the  walls   of   the  vessels  which   contain   them? 
We  have  found   that   in  an  ordinary  room  the  air  presses 
against  the  walls  with  a  force  of  15  pounds  to  the  square 


KINETIC  THEORY  OF  GASES  51 

inch.  Within  an  automobile  tire  this  pressure  may  amount 
to  as  much  as  100  pounds,  and  the  steam  pressure  within  the 
boiler  of  an  engine  is  often  as  high  as  240  pounds  per  square 
inch.  Yet  in  all  these  cases  we  may  be  certain  that  the  mole- 
cules of  the  gas  are  separated  from  each  other  by  distances 
which  are  large  in  comparison  with  the  diameters  of  the  mole- 
cules ;  for  when  we  reduce  steam  to  water,  it  shrinks  to  16100 
of  its  original  volume,  and  when  we  reduce  air  to  the  liquid 
form,  it  shrinks  to  about  -g-i-^  of  its  ordinary  volume. 

The  explanation  is  at  once  apparent  when  we  reflect  upon 
the  motions  of  the  molecules.  For  just  as  a  stream  of  water 
particles  from  a  hose  exerts  a  continuous  force  against  a  wall 
on  which  it  strikes,  so  the  blows  which  the  innumerable 
molecules  of  a  gas  strike  against  the  walls  of  the  containing 
vessel  must  constitute  a  continuous  force  tending  to  push 
out  these  walls.  In  this  way  we  account  for  the  fact  that 
vessels  containing  only  gas  do  not  collapse  under  the  enor- 
mous external  pressures  to  which  we  know  them  to  be 
subjected.  A  soap  bubble  6i  inches  in  diameter  is,  at  normal 
atmospheric  pressure,  under  a  total  crushing  force  of  one  ton. 

65.  Explanation  of  Boyle's  law.  It  will  be  remembered 
that  it  was  discovered  in  the  last  chapter  that  when  the  den- 
sity of  a  gas  is  doubled,  the  temperature  remaining  constant, 
the  pressure  is  found  to  double  also ;  when  the  density  was 
trebled,  the  pressure  was  trebled ;  etc.  This,  in  fact,  was  the 
assertion  of  Boyle's  law.  Now  this  is  exactly  what  would  be 
expected  if  the  pressure  which  a  gas  exerts  against  a  given 
surface  is  due  to  blows  struck  by  an  enormous  number  of 
swiftly  moving  molecules ;  for  doubling  the  number  of  mole- 
cules in  the  given  space,  that  is,  doubling  the  density,  would 
simply  double  the  number  of  blows  struck  per  second  against 
that  surface,  and  hence  would  double  the  pressure.  The 
kinetic  theory  of  gases  which  is  here  presented  accounts  in 
this  simple  way  for  Boyle's  law. 


52  MOLECULAR  MOTIONS 

66.  Brownian   movements   and   molecular  motions.     It  has  recently 
been  found  possible  to  demonstrate  the  existence  of  molecular  motions 
in  gases  in  a  very  direct  and  striking  way.   It  is  found  that  very  minute 
oil  drops  suspended  in  perfectly  stagnant  air,  instead  of  being  them- 
selves at  rest,  are  ceaselessly  dancing  about  just  as  though  they  were 
endowed  with  life.    In  1913  it  was  definitely  proved  that  these  mo- 
tions, which  are    known  as   the   Brownian  movements,  are   the    direct 
result  of  the  bombardment  which  the  droplets  receive  from  the  flying 
molecules  of  the  gas  with  which  they  are  surrounded;  for  at  a  given 
instant  this  bombardment  is  not  the  same  on  all  sides,  and  hence 
the  suspended  particle,  if  it  is  minute  enough,  is  pushed  hither  and 
thither  according  as  the  bombardment  is  more  intense  first  in  one 
direction,  then  in  another.    There  can  be  no  doubt  that  what  the  oil 
drops  are  here  seen  to  be  doing,  the  molecules  themselves  are  also  doing, 
only  in  a  much  more  lively  way. 

67.  Molecular  velocities.    From  the  known  weight  of  a  cubic  centi- 
meter of  air  under  normal  conditions,  and  the  known  force  which  it 
exerts  per  square  centimeter   (namely,  1033  grams),  it  is  possible  to 
calculate  the  velocity  which  its  molecules  must  possess  in  order  that 
they  may  produce  by  their  collisions  against  the  walls  this  amount 
of  force.    The  result  of  the  calculation  gives  to  the  air  molecules  under 
normal  conditions  a  velocity  of  about  445  meters  per  second,  while  it 
assigns  to  the  hydrogen  molecules  the  enormous  speed  of  1700  meters 
(a  mile)  per  second.    The  speed  of  a  projectile  is  seldom  greater  than 
800  meters  (2500  feet)  per  second.    It  is  easy  to  see,  then,  since  the 
molecules  of  gases  are  endowed  with  such  speeds,  why  air,  for  example, 
expands  instantly  into  the  space  left  behind  by  the  rising  piston  of  the 
air  pump,  and  why  any  gas  always  fills  completely  the  vessel  which 
contains  it  (see  mercury-diffusion  air  pump,  opposite  page  33). 

68.  Diffusion  of  gases  through  porous  walls.     Strong  evi- 
dence for  the  correctness  of  the  above  views  is  furnished  by 
the  following  experiment : 

Let  a  porous  cup  of  unglazed  earthenware  be  closed  with  a  rubber 
stopper  through  which  a  glass  tube  passes,  as  in  Fig.  54.  Let  the  tube 
be  dipped  into  a  dish  of  colored  water,  and  a  jar  containing  hydrogen 
placed  over  the  porous  cup ;  or  let  the  jar  simply  be  held  in  the  position 
shown  in  the  figure,  and  let  illuminating  gas  be  passed  into  it  by  means 
of  a  rubber  tube  connected  with  a  gas  jet.  The  rapid  passage  of  bubbles 
out  through  the  water  will  show  that  the  gaseous  pressure  inside  the 


MOLECULAR  MOTIONS  IN  LIQUIDS 


53 


cup  is  rapidly  increasing.  Now  let  the  bell  jar  be  lifted,  so  that  the 
hydrogen  is  removed  from  the  outside.  Water  will  at  once  begin  to  rise 
in  the  tube,  showing  that  the  inside  pressure  is  now  rapidly  decreasing- 

The  explanation  is  as  follows  :  We  have 
learned  that  the  molecules  of  hydrogen  have 
about  four  times  the  velocity  of  the  mole- 
cules of  air.  Hence,  if  there  are  as  many 
hydrogen  molecules  per  cubic  centimeter 
outside  the  cup  as  there  are  air  molecules 
per  cubic  centimeter  inside,  the  hydrogen 
molecules  will  strike  the  outside  of  the  wall 
four  times  as  frequently  as  the  air  molecules 
will  strike  the  inside.  Hence,  in  a  given 
time  the  number  of  hydrogen  molecules 
which  pass  into  the  interior  of  the  cup 
through  the  little  holes  in  the  porous  mate- 
rial is  four  times  as  great  as  the  num- 
ber of  air  particles  which  pass  out ;  hence 
the  pressure  within  increases.  When  the  bell  jar  is  removed, 
the  hydrogen  which  has  passed  inside  begins  to  pass  out  faster 
than  the  outside  air  passes  in,  and  hence  the  inside  pressure  is 
diminished. 

MOLECULAR  MOTIONS  IN  LIQUIDS 

69.  Molecular  motions  in  liquids  and  evaporation.  Evidence 
that  the  molecules  of  liquids  as  well  as  those  of  gases  are  in  a 
state  of  perpetual  motion  is  found,  first,  in  the  familiar  facts 
of  evaporation. 

We  know  that  the  molecules  of  a  liquid  in  an  open  vessel 
are  continually  passing  off  into  the  space  above,  for  it  is  only 
a  matter  of  time  when  the  liquid  completely  disappears  and  the 
vessel  becomes  dry.  Now  it  is  hard  to  imagine  a  way  in  which 
the  molecules  of  a  liquid  thus  pass  out  of  the  liquid  into  the 
space  above,  unless  these  molecules,  while  in  the  liquid  condition, 


FIG.  54.     Diffusion 

of  hydrogen  through 

porous  cup 


54  MOLECULAR  MOTIONS 

are  in  motion.  As  soon,  however,  as  such  a  motion  is  assumed, 
the  facts  of  evaporation  become  perfectly  intelligible.  For  it  is 
to  be  expected  that  in  the  jostlings  and  collisions  of  rapidly 
moving  liquid  molecules  an  occasional  molecule  will  acquire  a 
velocity  much  greater  than  the  average.  This  molecule  may 
then,  because  of  the  unusual  speed  of  its  motion,  break  away 
from  the  attraction  of  its  neighbors  and  fly  off  into  the  space 
above.  This  is  indeed  the  mechanism  by  which  we  now  believe 
that  the  process  of  evaporation  goes  on  from  the  surface  of 
any  liquid. 

70.  Molecular  motions  and  the  diffusion  of  liquids.  One  of 
the  most  convincing  arguments  for  the  motions  of  molecules 
in  gases  was  found  in  the  fact  of  diffusion. 
But  precisely  the  same  sort  of  phenomena  are 
observable  in  liquids. 

Let  a  few  lumps  of  blue  litmus  be  pulverized  and 
dissolved  in  water.  Let  a  tall  glass  cylinder  be  half 
filled  with  this  water  anc|,  a  few  drops  of  ammonia 
added.  Let  the  remainder  of  the  litmus  solution  be 
turned  red  by  the  addition  of  one  or  two  cubic  centi- 
meters of  nitric  acid.  Then  let  this  acidulated  water 
be  introduced  into  the  bottom  of  the  jar  through  a  FIG.  55.  Diffusion 
thistle  tube  (Fig.  55).  In  a  few  minutes  the  line  of  of  liquids 

separation  between  the  acidulated  water  and  the  blue 
solution  will  be  fairly  sharp ;  but  in  the  course  of  a  few  hours,  even 
though  the  jar  is  kept  perfectly  quiet,  the  red  color  will  be  found  to  have 
spread  considerably  toward  the  top,  showing  that  the  acid  molecules  have 
gradually  found  their  way  up. 

Certainly,  then,  the  molecules  of  a  liquid  must  be  endowed 
with  the  power  of  independent  motion.  Indeed,  every  one  of 
the  arguments  for  molecular  motions  in  gases  applies  with 
equal  force  to  liquids.  Even  the  Brownian  movements  can 
be  seen  in  liquids,  though  they  are  here  so  small  that  high- 
power  microscopes  must  be  used  to  make  them  apparent. 


MOLECULAR  MOTIONS  IN   SOLIDS  55 

MOLECULAR  MOTIONS  IN  SOLIDS 

71.  Molecular  motions  and  the  diffusion  of  solids.    It  has 
recently  been  demonstrated  that  if  a  layer  of  lead  is  placed 
upon  a  layer  of  gold,  molecules  of  gold  may  in  time  be  de- 
tected throughout  the  whole  mass  of  the  lead.    This  diffusion 
of  solids  into  one  another  at  ordinary  temperature  has  been 
shown  only  for  these  two  metals,  but  at  higher  temperatures 
(for  example,  500°  C.)  all  of  the  metals  show  the  same  char- 
acteristics to  quite  a  surprising  degree. 

The  evidence  for  the  existence  of  molecular  motions  in 
solids  is,  then,  no  less  strong  than  in  the  case  of  liquids. 

72.  The   three   states  of   matter.     Although   it  has   been 
shown  that,  in  accordance  with  current  belief,  the  molecules  of 
all  substances  are  in  very  rapid  motion,  yet  differences  exist 
in  the  kind  of  motion  which  the  molecules  in  the  three  states 
possess.    Thus,  in  the  solid  state  it  is  probable  that  the  mole- 
cules oscillate  with  great  rapidity  about  certain  fixed  points, 
always  being  held  by  the  attractions  of  their  neighbors,  that 
is,  by  the  cohesive  forces  (see  §  112),  in  very  nearly  the  same 
positions  with  reference  to  other  molecules  in  the  body.    In 
rare   instances,  however,  as  the   facts   of   diffusion   show,  a 
molecule  breaks  away  from  its  constraints.    In   liquids,   on 
the  other  hand,  while  the  molecules  are,  in  general,  as  close 
together  as  in  solids,  they  slip  about  with  perfect  ease  over 
one  another  and  thus  have  no  fixed  positions.    This  assump- 
tion is  necessitated  by  the  fact  that  liquids  adjust  themselves 
readily  to  the  shape  of  the.  containing  vessel.    In  gases  the 
molecules  are  comparatively  far  apart,  as  is  evident  from  the 
fact  that  a  cubic  centimeter  of  water  occupies  about  1600 
cubic  centimeters  when  it  is  transformed  into  steam ;   and, 
furthermore,  they  exert  almost  no  cohesive  force  upon   one 
another,  as  is  shown  by  the  indefinite  expansibility  of  gases. 


56  MOLECULAK  MOTIONS 


QUESTIONS  AND  PROBLEMS 

1.  If  a  vessel  with  a  small  leak  is  filled  with  hydrogen  at  a  pressure 
of  2  atmospheres,  the  pressure  falls  to  1  atmosphere  about  four  times 
as  fast  as  when  the  same  experiment  is  tried  with  air.    Can  you  see  a 
reason  for  this? 

2.  What  is  the  density  of  the  air  within  an  automobile  tire  that  is 
inflated  to  a  pressure  of  80  Ib.  per  square  inch  ?  (1  atmosphere  =  14.7  Ib. 
per  sq.  in.) 

3.  A  liter  of  air  at  a  pressure  of  76  cm.  is  compressed  so  as  to  occupy 
400  cc.    What  is  the  pressure  against  the  walls  of  the  containing  vessel? 

4.  If  an  open  vessel  contains  250  g.  of  air  when  the  barometric  height 
is  750  mm.,  what  weight  will  the  same  vessel  contain  at  the  same  tem- 
perature when  the  barometric  height  is  740  mm.? 

5.  Find  the  pressure  to  which  the  diver  was  subjected  who  descended 
to  a  depth  of  304  ft.    Find  the  density  of  the  air  in  his  suit,  the  density 
at  the  surface  being  .00128  g.  per  cubic  centimeter  and  the  temperature 
being  assumed  to  remain  constant.    Take  the  pressure  at  the  surface 
as  30  in. 

6.  A  bubble  of  air  which  escaped  from  this  diver's  suit  would  increase 
to  how  many  times  its  volume  on  reaching  the  surface? 

7.  Salt  is  heavier  than  water.    Why  does  not  all  the  salt  in  a  mixture 
of  salt  and  water  settle  to  the  bottom? 


CHAPTER  V 

FORCE  AND  MOTION 
DEFINITION  AND  MEASUREMENT  OF  FORCE 

73.  Distinction  between  a  gram  of  mass  and  a  gram  of  force. 
If  a  gram  of  mass  is  held  in  the  outstretched  hand,  a  down- 
ward pull  upon  the  hand  is  felt.    If  the  mass  is  50,000  g.  in- 
stead of  1,  this  pull  is  so  great  that  the  hand  cannot  be  held 
in  place.    The  cause  of  this  pull  we  assume  to  be  an  attractive 
force  which  the  earth  exerts  on  the  matter  held  in  the  hand, 
and  we  define  the  gram  of  force  as  the  amount  of  the  earths  pull 
at  its  surface  upon  one  gram  of  mass. 

Unfortunately,  in  ordinary  conversation  we  often  fail  alto- 
gether to  distinguish  between  the  idea  of  mass  and  the  idea 
of  force,  and  use  the  same  word  "  gram  "  to  mean  sometimes 
a  certain  amount  of  matter  and  at  other  times  the  pull  of  the 
earth  upon  this  amount  of  matter.  That  the  two  ideas  are,  how- 
ever, wholly  distinct  is  evident  from  the  consideration  that 
the  amount  of  matter  in  a  body  is  always  the  same,  no  matter 
where  the  body  is  in  the  universe,  while  the  pull  of  the  earth 
upon  that  amount  of  matter  decreases  as  we  recede  from  the 
earth's  surface.  It  will  help  to  avoid  confusion  if  we  reserve 
the  simple  term  "  gram  "  to  denote  exclusively  an  amount  of 
matter  (that  is,  a  mass)  and  use  the  full  expression  "  gram  of 
force  "  wherever  we  have  in  mind  the  pull  of  the  earth  upon 
this  mass. 

74.  Method  of  measuring  forces.    When  we  wish  to  com- 
pare accurately  the  pulls  exerted  by  the  earth  upon  different 
masses,   we   find  such   sensations  as   those   described  in  the 

57 


58 


FORCE  AND  MOTION 


preceding  paragraph  very  untrustworthy  guides.   An  accurate 
method,  however,  of  comparing  these  pulls  is  that  furnished 
by  the  stretch  produced  in  a  spiral  spring.    Thus,  the  pull  of 
the  earth  upon  a  gram  of  mass  at  its  sur- 
face   will   stretch   a  given   spring  a  given 
distance,  ab  (Fig.  56) ;  the  pull  of  the  earth 
upon  2  grams  of  mass  is  found  to  stretch  the 
spring  a  larger  distance,  ac\  upon  3  grams,  a 
still  larger   distance,  ad;  etc.    In  order  to 
graduate  a  spring  balance  (Fig.  57)  so  that 
it  will  thenceforth  measure  the  values  of  any 
pulls  exerted  upon  it,  no  matter  how  these 
pulls  may  arise,  we  have  only  to  place  a  fixed    -pIG  55    Method  of 
surface  behind  the  pointer  and  make  lines      measuring  forces 
upon  it  corresponding  to  the  points  to  which 
it  is  stretched  by  the  pull  of  the  earth  upon  different  masses. 
Thus,  if  a  man  stretch  the  spring  so  that  the  pointer  is  opposite 
the  mark  corresponding  to  the  pull  of  the  earth 
upon  2  grams  of  mass,  we  say  that  he  exerts 
2  grams  of  force ;  if  he  stretch  it  the  distance 
corresponding  to  the  pull  of  the  earth  upon  3 
grams  of  mass,  he  exerts  3  grams  of  force ;  etc. 
The  spring  balance  thus  becomes  an  instrument 
for  measuring  forces. 

75.  The  gram  of  force  varies  slightly  in  differ- 
ent localities.  With  the  spring  balance  it  is  easy 
to  verify  the  statement  made  above,  that  the 
force  of  the  earth's  pull  decreases  as  we  recede 
from  the  earth's  surface ;  for  upon  a  high  moun- 
tain the  stretch  produced  by  a  given  mass  is  indeed  found 
to  be  slightly  less  than  at  sea  level.  Furthermore,  if  the 
balance  is  simply  carried  from  point  to  point  over  the  earth's 
surface,  the  stretch  is  still  found  to  vary  slightly.  For  ex- 
ample, at  Chicago  it  is  about  one  part  in  1000  less  than  it 


FIG.  57.    The 

spring  balance 


COMPOSITION  AND  RESOLUTION  OF  FORCES     59 

is  at  Paris,  and  near  the  equator  it  is  five  parts  in  1000  less 
than  it  is  near  the  pole.  This  is  due  in  part  to  the  earth's 
rotation  and  in  part  to  the  fact  that  the  earth  is  not  a  perfect 
sphere  and  that  in  going  from  the  equator  toward  the  pole 
we  are  coming  nearer  and  nearer  to  the  center  of  the  earth. 
We  see,  therefore,  that  the  weight  of  one  gram  of  mass  is  not  an 
absolutely  definite  unit  of  force.  One  gram  of  force  is,  strictly 
speaking,  the  weight  of  one  gram  of  mass  in  latitude  45°  at 
sea  level. 

COMPOSITION  AND  RESOLUTION  or  FORCES 

76.  Graphic  representation  of  force.    A  force  is  completely 
described  when  its  magnitude,  its  direction,  and  the  point  at 
which  it  is  applied  are  given.    Since  the  three  characteristics  of 
a  straight  line  are  its  length,  its  direction,  and  the  point  at 
which    it   starts,   it    is    obviously  possible   to 

represent  forces  by  means  of  straight  lines.      A^ 

Thus,  if  we  wish  to  represent  the  fact  that     FlG-  58<  GraPhic 
r  f.    0  -.  .         .  ,         representation  of 

a  force  ot    8   pounds,   acting  in  an  easterly        a  gingle  force 

direction,  is  applied  at  the  point  A  (Fig.  58), 
we  draw  a  line  8  units  long,  beginning  at  the  point  A  and 
extending  to  the  right.  The  length  of  this  line  then  repre- 
sents the  magnitude  of  the  force ;  the  direction  of  the  line, 
the  direction  of  the  force ;  and  the  starting  point  of  the  line, 
the  point  at  which  the  force  is  applied. 

77.  Resultant  of  two  forces  acting  in  the  same  line.     The 
resultant  of  two  forces  is  defined  as  that  single  force  which  will 
produce  the  same  effect  upon  a  body  as  is  produced  by  the  joint 
action  of  the  two  forces. 

If  two  spring  balances  are  attached  to  a  small  ring  and 
pulled  in  the  same  direction  until  one  registers  10  g.  of  force 
and  the  other  5,  it  will  be  found  that  a  third  spring  balance 
attached  to  the  same  point  and  pulled  in  the  opposite  direc- 
tion will  register  exactly  15  g.  when  there  is  equilibrium ; 


60 


FORCE  AND  MOTION 


that  is,  the  resultant  of  two  parallel  forces  acting  in  the  same 
direction  is  equal  to  the  sum  of  the  two  forces. 

Similarly,  the  resultant  of  two  oppositely  directed  forces  applied 
at  the  same  point  is  equal  to  the  difference  between  them,  and  its 
direction  is  that  of  the  greater  force. 

78.  Equilibrant.    In  the  last  experiment  the  pull  in  the 
spring  balance  which  registered  15  g.  was  not  the  resultant 
of  the  5  g.  and  10  g.  forces  ;  it  was  rather  a  force  equal  and 
opposite  to  that  resultant.    Such  a  force  is  called  an  equilibrant. 
The  equilibrant  of  a  force  or  forces  is  that 

single  force  ivhich  will  just  prevent  the  motion 
which  the  given  forces  tend  to  produce.  It  is 
equal  and  opposite  to  the  resultant  and  has 
the  same  point  of  application.  2~" 

79.  The  resultant  of  forces  acting  at  an    FIG.  59.   Direction 
angle  (concurrent  forces).     If  a  body  at  A     of  resultant  of  two 
is  pulled  toward  the  east  with  a  force  of     equal  f^gat  ' 

10  Ib.  (represented  in  Fig.  59  by  the  line 

AC)   and  toward  the    north  with   a  force   of   10  Ib.   (repre- 

sented in  the  figure   by  the  line  AIT),  the   effect  upon  the 

motion  of  the  body  must,  of  course,  be  the  same  as  though 

some   single   force    acted    somewhere 

between    AC  and   AB.     If  the  body 

moves   under   the   action   of   the   two 

equal   forces,   it    may    be   seen    from 

symmetry   that  it  must   move    along 

a  line  midway  between  AC  and  AB, 

that  is,  along  the  line  AR.    This  line, 

therefore,  indicates  the  direction  as  well  as  the  point  of  appli- 

cation of  the  resultant  of  the  forces  AC  and  AB. 

If  the  two  forces  are  not  equal,  as  in  Fig.  60,  then  the 
resultant  will  lie  nearer  the  larger  force.  The  following 
experiment  will  show  the  relation  between  the  two  forces 
and  their  resultant, 


6Q    The  resultant  Iies 
nearer  the  larer  force 


COMPOSITION  AND  RESOLUTION  OF  FORCES     61 


FIG.  61.    Experimental  proof 
of  parallelogram  law 


Let  the  rings  of  two  spring  balances  be  hung  over  nails  B  and  C  in 
the  rail  at  the  top  of  the  blackboard  (Fig.  61),  and  let  a  weight  W  be 
tied  near  the  middle  of  the  string  joining  the  hooks  of  the  two  balances. 
The  weight  W  is  not  supported  by  the 
pull  of  the  balance  E  or  by  that  of 
F;  it  is  supported  by  their  resultant, 
which  evidently  must  act  vertically  up- 
ward, since  the  only  single  force  capable 
of  supporting  the  weight  W  is  one  that 
is  equal  and  opposite  to  W.  Let  the  lines 
OA  and  OD  be  drawn  upon  the  black- 
board behind  the  string,  and  upon  these 
lines  lay  off  the  distances  Oa  and  Ob, 
which  contain  as  many  units  of  length 
as  there  are  units  of  force  indicated  by 
the  balances  E  and  F  respectively.  Simi- 
larly, on  a  vertical  line  from  0  lay  off  the 
exact  distance  OR  required  to  represent 

the  force  that  supports  the  weight.  This,  as  noted  above,  represents  the 
resultant.  Now  let  a  parallelogram  be  constructed  upon  Oa  and  Ob  as 
sides.  The  line  OR  already  drawn  will  be  the  diagonal. 

Hence,  to  find  graphically  the  resultant  of  two  concurrent 
forces,  (.?)  represent  the  concurrent  forces,  (2)  construct  upon  them 
as  sides  a  parallelogram,  and  (3)  draw  a  diagonal  from  the  point 
of  application.  This  diagonal  represents  the  point  of  application, 
direction,  and  magnitude  of  the  resultant. 

80.  Component  of  a  force.  When- 
ever a  force  acts  upon  a  body  in  some 
direction  other  than  that  in  which  the 
body  is  free  to  move,  it  is  clear  that 
the  full  effect  of  the  force  cannot  be 
spent  in  producing  motion.  For  ex- 
ample, suppose  that  a  force  is  applied 

in  the  direction  OR  (Fig.  62)  to  a  car  on  an  elevated  track. 
Evidently  OR  produces  two  distinct  effects  upon  the  car :  on 
the  one  hand,  it  moves  the  car  along  the  track;  and,  on  the 
other,  it  presses  it  down  against  the  rails.  These  two  effects 


R 


FIG.  62.    Component  of 
a  force 


62 


FORCE  AND  MOTION 


might  be  produced  just  as  well  by  two  separate  forces  acting 
in  the  directions  OA  and  OB  respectively.  The  value  of  the 
single  force  which,  acting  in  the  direction  OA,  will  produce 
the  same  motion  of  the  car  on  the  track  as  is  produced  by 
OR,  is  called  the  component  of  OR  in  the  direction  OA.  Simi- 
larly, the  value  of  the  single  force  which,  acting  in  the  direc- 
tion OB,  will  produce  the  same  pressure  against  the  rails  as 
is  produced  by  the  force  OR,  is  called  the  component  of  OR 
in  the  direction  OB.  In  a  word,  the  component  of  a  force  in  a 
given  direction  is  the  effective  value  of  the  force  in  that  direction. 
81.  Magnitude  of  the  component  of  a  force  in  a  given  direc- 
tion. Since,  from  the  definition  of  component  just  given, 
the  two  forces,  one  to  be  applied  in  the  direction  OA  and 
the  other  in  the  direction  OB,  are  together  to  be  exactly 
equivalent  to  OR  in  their  effect  on  the  car,  their  magnitudes 
must  be  represented 
by  the  sides  of  a  par- 
allelogram of  which 
OR  is  the  diagonal. 
For  in  §  79  it  was 
shown  that  if  any  one 
force  is  to  have  the 
same  effect  upon  a 
body  as  two  forces  acting  simultaneously,  it  must  be  repre- 
sented by  the  diagonal  of  a  parallelogram  the  sides  of  which 
represent  the  two  forces.  Hence,  conversely,  if  two  forces  are 
to  be  equivalent  in  their  joint  effect  to  a  single  force,  they 
must  be  sides  of  the  parallelogram  of  which  the  single  force 
is  the  diagonal.  Hence  the  following  rule :  To  find  the  com- 
ponent of  a  force  in  any  given  direction,  represent  the  force  by 
a  line;  then,  using  the  line  as  a  diagonal,  construct  upon  it  a 
rectangle  the  sides  of  which  are  respectively  parallel  and  perpen- 
dicular to  the  direction  of  the  required  component.  The  length  of 
the  side  which  is  parallel  to  the  given  direction  represents  the 


FIG.  63.    Horizontal  component  of  pull  on  a  sled 


COMPOSITION  AND  RESOLUTION  OF  FORCES     63 

magnitude  of  the  component  which  is  sought.  Thus,  in  Fig.  62 
the  line  Om  completely  represents  the  component  of  OR  in 
the  direction  OA,  and  the  line  On  represents  the  component 
of  OR  in  the  direction  OB. 

Again,  when  a  boy  pulls  on  a  sled  with  a  force  of  10  Ib. 
in  the  direction  OR  (Fig.  63),  the  force  with  which  the  sled 
is  urged  forward  is  represented  by  the  length  of  Om,  which 
is  seen  to  be  but  9.3  Ib.  instead  of  10  Ib.  The  component 
which  tends  to  lift  the  sled  is  represented  by  On. 

To  apply  the  test  of  experiment  to  the  conclusions  of  the  preceding 
paragraph,  let  a  wagon  be  placed  upon  an  inclined  plane  (Fig.  64),  the 
height  of  which,  be,  is  equal  to  one  half  its  length  ab.  In  this  case 
the  force  acting  on  the  wagon  is  the  weight  of  the  wagon,  and  its 
direction  is  downward.  Let  this  force  be  represented  by  the  line  OR. 
Then,  by  the  construction  of  the  preceding  paragraph,  the  line  Om  will 
represent  the  value  of  the  force  which  is  pulling  the  carriage  down  the 
plane,  and  the  line  On  the  value  of  the 
force  which  is  producing  pressure  against 
the  plane.  Now,  since  the  triangle  ROm  is 
similar  to  the  triangle  abc  (for  ZmOR  = 
Z  abc,  Z  RmO  =  Z  acb,  and  Z  ORm  = 
we  have 

Om  _  bc^ 
OR  ~  ab' 

FIG.  64.     Component  of 

that  is,  in  this  case,  since  be  is  equal  to  one       weight  parallel  to  an  in- 
half  of  ab,  Om  is  one  half  of  OR.  Therefore  clined  plane 
the  force  which  is  necessary  to  prevent  the 

wagon  from  sliding  down  the  plane  should  be  equal  to  one  half  its  weight. 
To  test  this  conclusion  let  the  wagon  be  weighed  on  the  spring  balance 
and  then  placed  on  the  plane  in  the  manner  shown  in  the  figure.  The 
pull  indicated  by  the  balance  will,  indeed,  be  found  to  be  one  half  the 
weight  of  the  wagon. 

The  equation  Om/OR  =  bc/ab  gives  us  the  following  rule  for  finding 
the  force  necessary  to  prevent  a  body  from  moving  down  an  inclined 
plane,  namely,  the  force  which  must  be  applied  to  a  body  to  hold  it  in  place 
upon  an  inclined  plane  bears  the  same  ratio  to  the  weight  of  the  body  as  the 
height  of  the  plane  bears  to  its  length. 


64 


FORCE  A]STD  MOTION 


82.  Component  of  gravity  effective  in  producing  the  motion 
of  the  pendulum.  When  a  pendulum  is  drawn  aside  from  its 
position  of  rest  (Fig.  65),  the  force  acting  on  the  bob  is  its 
weight,  and  the  direction  of  this  force  is  vertical.  Let  it  be 
represented  by  the  line  OR.  The 
component  of  this  force  in  the 
direction  in  which  the  bob  is  free 
to  move  is  On,  and  the  component 
at  right  angles  to  this  direction  is 
Om.  The  second  component  Om 
simply  produces  stretch  in  the 
string  and  pressure  upon  the  point 
of  suspension.  The  first  compo- 
nent On  is  alone  responsible  for 
the  motion  of  the  bob.  A  consid- 
eration of  the  figure  shows  that 
this  component  becomes  larger 
and  larger  the  greater  the  dis- 
placement of  the  bob.  When  the 
bob  is  directly  beneath  the  point  of  support,  the  component 
producing  motion  is  zero.  Hence  a  pendulum  can  be  per- 
manently at  rest  only  when  its  bob  is  directly  beneath  the 
point  of  suspension.* 


FIG.  65.    Force    acting   on    dis- 
placed pendulum 


QUESTIONS  AND  PROBLEMS 

1.  The  engines  of  a  steamer  can  drive  it  12  mi.  per  hour.    How  fast 
can  it  go  up  a  stream  in  which  the  current  is  3  mi.  per  hour  ?   How  fast 
can  it  come  down  the  same  stream  ? 

2.  The  wind  drives  a  steamer  east  with  a  force  which  would  carry  it 
12  mi.  per  hour,  and  its  propeller  is  driving  it  south  with  a  force  which 
would  carry  it  15  mi.  per  hour.   What  distance  will  it  actually  travel  in 
an  hour  ?    Draw  a  diagram  to  represent  the  exact  path. 

*  It  is  recommended  that  the  study  of  the  laws  of  the  pendulum  be  intro- 
duced into  the  laboratory  work  at  about  this  point  (see  Experiment  12, 
authors'  Manual). 


COMPOSITION  AND  RESOLUTION  OF  FORCES     65 


3.  A  barge  is  anchored  in  a  river  during  a  storm.    If  the  wind  acts 
eastward  on  it  with  a  force  of  3000  lb.  and  the  tide  northward  with  a 
force  of  4000  lb.,  what  is  the  direction  and  magnitude  of  the  equilibrant ; 
that  is,  the  pull  of  the  anchor  cable  upon  the  barge? 

4.  A  picture  weighing  20  lb.  hangs  upon  a  cord  whose  parts  make 
an.  angle  of  120°  with  each  other.    Find  the  tension  (pull)  upon  each 
part  of  the  cord. 

5.  If  the  barrel  of  Fig.  66 
weighs    200  lb.,    with    what 
force  must  a  man  push  par- 
allel to  the  skid  to  keep  the 
barrel  in  place  if  the  skid  is 
9  ft.  long  and  the  platform 
3  ft.  high? 

6.  A  cake  of  ice  weighing 
200  lb.  is  held  at  rest  upon  an 

inclined  plane  12  ft.  long  and     FIG>  66.    Force  necessary  to  prevent  a  bar- 
3  ft.  high.   By  the  resolution-        rel  from  rolling  down  an  inclined  plane 
and-proportion  method   find 

the  component  of  its  weight  that  tends  to  make  the  ice  slide  down  the 
incline.  With  what  force  must  one  push  to  keep  the  ice  at  rest  ?  How 
great  is  the  component  that  tends  to  break  the  incline  ? 

7.  A  tight-rope  20  ft.  long  is  depressed  1  ft.  at  the  center  when 
a  man  weighing  120  lb.  stands  upon  it.     Determine  graphically  the 
tension  in  the  rope. 

8.  The  anchor  rope  of  a  kite  balloon  makes  an  angle  of  60°  with 
the  surface  of  the  earth.   If  the  lifting  power  of  the  balloon  is  1000  lb., 
find  the  pull  of  the  balloon  on  the  rope  and  the  horizontal  force  of 
the  wind  against  the  balloon. 

9.  A  canal  boat  and  the  engine  towing  it  move  in  parallel  paths 
which  are  50  ft.  apart.     The  tow  rope  is  130  ft.  long,  and  the  force 
(effort)     applied    to 

the  end  of  the  rope 
is  1300  lb.  Find  what 
component  of  the 
loOOlb.  acts  parallel 
to  the  path  of  the 
boat. 

10.  In  Fig.  6 7  the 
line     on     represents  FIG.  67.   Forces  acting  on  a  kite 

the  pull   of   gravity 

on  a  kite,  and  the  line  om  represents  the  pull  of  the  boy  on  the  string. 
What  is  the  name  given  to  the  force  represented  by  the  line  oRI 


FORCE  AND  MOTION 


FIG.  68.    Forces  acting  on  an  aeroplane 
in  flight 


11.  If  the  force  of  the  wind  against  the  kite  is  represented  by  the 
line  AB,  and  it  is  considered  to  be  applied  at  o,  what  must  be  the  relation 
between  the  force  oR  and  the 

component  of   AB  parallel   to  n   s 

,,      ,  .,     .     .  .,.,  Direction  of  Flight 

oR  when  the  kite  is  in  equilib- 
rium under  the  action  of  the 
existing  forces? 

12.  If    the    wind    increases, 
why  does  the  kite  rise  higher  ? 

13.  Show  from  Fig.  68  what 
force  supports  an  aeroplane  in 
flight.    (Remember  that  oR,  the 
component  of  the  wind  pressure 
AB  perpendicular  to  the  plane, 

is  the  only  acting  force  out  of  which  a  support   for   the  aeroplane 
can  be  derived.)   (See  frontispiece  and  opposite  pp.  153,  316,  and  317.) 

GBAVITATION 

83.  Newton's  law  of  universal  gravitation.  In  order  to  ac- 
count for  the  fact  that  the  earth  pulls  bodies  toward  itself, 
and  at  the  same  time  to  account  for  the  fact  that  the  moon  and 
planets  are  held  in  their  respective  orbits  about  the  earth  and 
the  sun,  Sir  Isaac  Newton  (1642—1727)  (see  opposite  p.  84) 
first  announced  the  law  which  is  now  known  as  the  law  of 
universal  gravitation.  This  law  asserts  first  that  every  body  in 
the  universe  attracts  every  other  body  with  a  force  which  varies 
inversely  as  the  square  of  the  distance  between  the  two  bodies. 
This  means  that  if  the  distance  between  the  two  bodies  con- 
sidered is  doubled,  the  force  will  become  only  one  fourth  as 
great;  if  the  distance  is  made  three,  four,  or  five  times  as 
great,  the  force  will  be  reduced  to  one  ninth,  one  sixteenth, 
or  one  twenty-fifth  of  its  original  value ;  etc. 

The  law  further  asserts  that  if  the  distance  between  two 
bodies  remains  the  same,  the  force  with  which  one  body  attracts 
the  other  is  proportional  to  the  product  of  the  masses  of  the  two 
bodies.  Thus  we  know  that  the  earth  attracts  3  cubic  centi- 
meters of  water  with  three  times  as  much  force  as  it  attracts 


GRAVITATION  67 

1,  that  is,  with  a  force  of  3  grams.  We  know  also,  from  the 
facts  of  astronomy,  that  if  the  mass  of  the  earth  were  doubled, 
its  diameter  remaining  the  same,  it  would  attract  3  cubic  cen- 
timeters of  water  with  twice  as  much  force  as  it  does  at  pres- 
ent, that  is,  with  a  force  of  6  grams  (multiplying  the  mass 
of  one  of  the  attracting  bodies  by  3  and  that  of  the  other  by 
2  multiplies  the  forces  of  attraction  by  3  x  2,  or  6).  In  brief, 
then,  Newton's  law  of  universal  gravitation  is  as  follows  :  Any 
two  bodies  in  the  universe  attract  each  other  with  a  force  which 
is  directly  proportional  to  the  product  of  the  masses  and  inversely 
proportional  to  the  square  of  the  distance  between  them. 

Two  masses  of  1  gram  each  at  a  distance  apart  of  1  cm. 
attract  each  other  with  a  force  of  about  1  6,0 00,000.000  gram- 
The  masses  of  the  sun  and  the  earth  are  so  great  that  even 
though  93,000,000  miles  apart,  they  attract  each  other  with 
a  force  of  about  4,000,000,000,000,000,000  tons.  A  body 
weighing  100  pounds  on  the  earth  would  weigh  about  2700 
pounds  on  the  sun.  A  freely  falling  body  on  the  earth  drops 
16  feet  the  first  second,  while  on  the  sun  it  would  fall  27 
times  that  far  in  the  first  second,  or  432  feet.  On  the  moon 
we  should  weigh  1  of  what  we  do  on  the  earth;  we  could 
jump  6  times  as  high  and  should  fall  i  as  fast. 

84.  Variation  of  the  force  of  gravity  with  distance  above  the 
earth's  surface.  If  a  body  is  spherical  in  shape  and  of  uniform 
density,  it  attracts  external  bodies  with  the  same  force  as 
though  its  mass  were  concentrated  at  its  center.  Since,  there- 
fore, the  distance  from  the  surface  to  the  center  of  the  earth 
is  about  4000  miles,  we  learn  from  Newton's  law  that  the 
earth's  pull  upon  a  body  4000  miles  above  its  surface  is  but 
one  fourth  as  much  as  it  would  be  at  the  surface. 

It  will  be  seen,  then,. that  if  a  body  be  raised  but  a  few  feet 
or  even  a  few  miles  above  the  earth's  surface,  the  decrease  in 
its  weight  must  be  a  very  small  quantity,  for  the  reason  that 
a  few  feet  or  a  few  miles  is  a  small  distance  compared  with 


68  FORCE  AND  MOTION 

4000  miles.  As  a  matter  of  fact,  at  the  top  of  a  mountain 
4  miles  high  1000  grams  of  mass  is  attracted  by  the  earth 
with  998  grams  instead  of  1000  grams  of  force. 

85.  Center  of  gravity.    From  the  law  of  universal  gravita- 
tion it  follows  that  every  particle  of  a  body  upon  the  earth's 
surface  is  pulled  toward  the  earth.    It  is  evident  that  the  sum 
of  all  these  little  pulls  on  the  particles  of  which  the  body  is 
composed  must  be  equal  to  the  total  pull  of  the  earth  upon 
the  body.    Now  it  is  always  possible  to  find  one  single  point 
in  a  body  at  which  a  single  force,  equal  in  magnitude  to  the 
weight  of  the  body  and  directed  upward,  can  be  applied  so 
that  the  body  will  remain  at  rest  in  whatever  position  it  is 
placed.    This  point  is  called  the  center  of  gravity  of  the  body. 
Since  this  force  counteracts  entirely  the  earth's  pull  upon  the 
body,  it  must  be  equal  and  opposite  to  the  resultant  of  all 
the  small  forces  which  gravity  is  exerting  upon  the  different 
particles  of  the  body.    Hence  the  center  of  gravity  may  be  de- 
fined as  the  point  of  application  of  the  resultant  of  all  the  little 
downward  forces  of  gravity  acting  upon 

the  parts  of  the  body ;  that  is,  the  center  of 

gravity  of  a  body  is  the  point  at  which  the 

entire  weight  of  the  body  may  be  considered 

an  concentrated.    The  earth's  attraction  for 

a  body  is  therefore  always  considered  not 

as  a  multitude  of  little  forces  but  as  one 

single  force  F  (Fig.  69)  equal  to  the  pull    FIG.  69.    Center  of 

of  gravity  upon  the  body  and  applied  at  its 

center  of  gravity  G.    It  is  evident,  then,  that 

under  the  influence  of  the  earths  pull,  every  body  tends  to  assume 

the  position  in  which  its  center  of  gravity  is  as  low  as  possible. 

86.  Method  of   finding   center  of   gravity  experimentally. 
From  the  above  definition  it  will  be  seen  that  the  most  direct 
way  of  finding  the  center  of  gravity  of  any  flat  body,  like  that 
shown  in  Fig.  70,  is  to  find  the  point  upon  which  it  will  balance. 


GRAVITATION 


69 


Let  an  irregular  sheet  of  zinc  be  thus  balanced  on  the  point  of  a 
pencil  or  the  head  of  a  pin.  Let  a  small  hole  be  punched  through 
the  zinc  at  the  point  of  balance,  and  let  a  needle  be  thrust  through  this 
hole.  When  the  needle  is  held  hor- 
izontally, the  zinc  will  be  found  to 
remain  at  rest,  no  matter  in  what 
position  it  is  turned. 

To  illustrate  another  method  of 
finding  the  center  of  gravity  of 
the  zinc,  let  it  be  supported  from 
a  pin  stuck  through  a  hole  near 
its  edge,  that  is,  b  (Fig.  70).  Let 
a  plumb  line  be  hung  from  the 
pin,  and  let  a  line'  In  be  drawn 
through  1}  on  the  surface  of  the 

zinc  parallel  to  and  directly  behind  the  plumb  line.   Let  the  zinc  be  hung 
from  another  point  a,  and  let  another  line  am  be  drawn  in  a  similar  way. 


FIG.  70.   Locating  center  of  gravity 


Since  the  attraction  of  the  earth  for  a  body  may  be  con- 
sidered as  a  single  force  applied  at  the  center  of  gravity,  a 
suspended  body  (for  example,  the  sheet  of  zinc)  can  remain 
at  rest  only  when  the  center  of  gravity  is  directly  beneath  the 
point  of  support  (see  §  85).  It  must  therefore  lie  somewhere 
on  the  line  am.  For  the  same 
reason  it  must  lie  on  the  line  bn. 
But  the  only  point  which  lies  on 
both  of  these 
lines  is  their 
point  of  inter- 
section G.  The 
point  of  inter- 
section, then,  of 

any  two  vertical  lines  dropped  through  two  different  points  of 
suspension  locates  the  center  of  gravity  of  a  body. 

87.  Stable  equilibrium.  A  body  is  said  to  be  in  stable  equi- 
librium if  it  tends  to  return  to  its  original  position  when  very 
slightly  tipped,  or  rotated,  out  of  that  position.  A  pendulum, 


A  B  c  D 

FIG.  71.    Illustration  of  varying  degrees  of  stability 


70 


FOKCE  AND  MOTION 


a  chair,  a  cube  resting  on  its  side,  a  cone  resting  on  its  base, 
a  boat  floating  quietly  in  still  water,  are  all  illustrations. 

In  general,  a  body  is  in  stable  equilibrium  whenever  tip- 
ping it  slightly  tends  to  raise  its  center  of  gravity.  Thus,  in 
Fig.  71  all  of  the  bodies  A,  B,  (7,  Z>,  are  in  stable  equilibrium, 
for  in  order  to  overturn  any  one  of  them  its  center  of  gravity 


FIG.  72.    Quebec  bridge 

G  must  be  raised  through  the  height  ai.  If  the  weights  are 
all  alike,  that  one  will  be  most  stable  for  which  ai  is  greatest. 
In  building  cantilever  bridges  such  as  the  large  one  over  the 
St.  Lawrence  River  at  Quebec  (Fig.  72)  the  engineers  build 
out  the  cantilever  arms  equally  in  opposite  directions,  so  as  to 
keep  their  centers  of  gravity  constantly 
over  the  piers  until  the  parts  either  meet 
at  the  center  or  are  close  enough  to  receive 
the  central  span,  which  is  hoisted  to  place. 


The  condition  of  stable  equilibrium  for  bod- 
ies which  rest  upon  a  horizontal  plane  is  that  a 
vertical  line  through  the  center  of  gravity  shall 
fall  within  the  base,  the  base  being  defined  as 
the  polygon  formed  by  connecting  the  points  at 
which  the  body  touches  the  plane,  as  ABC 
(Fig.  73) ;  for  it  is  clear  that  in  such  a  case  a 
slight  displacement  must  raise  the  center  of 

gravity  along  the  arc  of  which  OG  is  the  radius.  If  the  vertical  line 
drawn  through  the  center  of  gravity  fall  outside  the  base,  as  in  Fig.  74, 
the  body  must  always  fall. 


B 


FIG.  73.  Body  in  stable 
equilibrium 


GRAVITATION  71 

The  condition  of  stable  equilibrium  for  bodies  supported  from  a  single 
point,  as  in  the  case  of  a  pendulum,  is  that  the  point  of  support  be  above 
the  center  of  gravity.  For  example,  the  beam  of  a  balance  cannot  be  in 
stable  equilibrium,  so  that  it  will  return  to  the 
horizontal  position  when  slightly  displaced,  un- 
less its  center  of  gravity  g  (Fig.  3,  p.  7)  is  below 
the  knife-edge  C.  (The  pans  are  not  to  be  con- 
sidered, since  they  are  not  rigidly  connected  to 
the  beam.) 

88.  Neutral  and  unstable  equilibrium. 

,     .         -i  ^     i       •  7          -TT    -  FIG  74.   Body  not  in 

A  body  is  said  to  be  in  neutral  equilibrium  equilibrium 

when,  after  a  slight  displacement,  it  tends 
neither  to  return  to  its  original  position  nor  to  move  farther 
from  it.  Examples  of  neutral  equilibrium  are  a  spherical  ball 
lying  on  a  smooth  plane,  a  cone  lying  on  its  side,  a  wheel  free 
to  rotate  about  a  fixed  axis  through  its  center,  or  any  body 
supported  at  its  center  of  gravity.  In  general,  a  body  is  in 
neutral  equilibrium  when  a  slight  displacement  neither  raises 
nor  lowers  its  center  of  gravity. 

A  body  is  in  unstable  equilibrium  when,  after  a  slight  tip- 
ping, it  tends  to  move  farther  from  its  original  position.  A 
cone  balanced  on  its  point  or  an  egg  on  its  end  are  examples. 
In  all  such  cases  a  slight  tipping  lowers  the  center  of  gravity, 
and  the  motion  then  continues  until  the  center  of  gravity  is  as 
low  as  circumstances  will  permit.  The  condition  for  unstable 
equilibrium  in  the  case  of  a  body  supported  by  a  point  is  that 
the  center  of  gravity  shall  be  above  the  point  of  support. 

QUESTIONS  AND  PROBLEMS 

1.  Explain  why  the  toy  shown  in  Fig.  75  will  not  lie  upon  its  side, 
but  rises  to  the  vertical  position.    Does  the  center  of  gravity  rise? 

2.  Where  is  the  center  of  gravity  of  a  hoop?  of  a  cubical  box?    Is 
the  latter  more  stable  when  empty  or  when  full  ?    Why  ? 

3.  Where  must  the  center  of  gravity  of  the  beam  of  a  balance  be 
with  reference  to  the  supporting  knife-edge  C?    (Fig.  3,  p.  7.)    Why? 
Could  you  make  a  weighing  if  C  and  g  coincided?   Why? 


72 


FORCE  AND  MOTION 


4.  What  is  the  object  of  ballast  in  a  ship? 

5.  What  is  the  most  stable  position  of  a  brick?  the  least  stable?  Why? 

6.  In  what  state  of  equilibrium  is  a  pendulum  at  rest?    Why? 

7.  What  purpose  is  served  by  the  tail  of  a  kite? 

8.  Do  you  get  more  sugar  to  the  pound  in  ;££\ 
Calcutta  than  in  Aberdeen  when  using  a  beam           *>j.( 
balance?  when  using  a  spring  balance?  Explain. 

9.  What  change  would  there  be  in  your 
weight  if  your  mass  were  to  become  four  times 
as  great  and  that  of  the  earth  three  times,  the 
radius  of  the  earth  remaining  the  same  ? 

10.  The  pull  of  the  earth  on  a  body  at  its  sur- 
face is  100  kg.  Find  the  pull  on  the  same  body  4000  mi.  above  the  surface ; 
1000  mi.  above  the  surface  ;  3  mi.  above  'the  surface.   (Take  the  earth's 
radius  as  4000  mi.) 

FALLING  BODIES 

89.  Galileo's  early  experiments.  Many  of  the  familiar  and 
important  experiences  of  our  lives  have  to  do  with  falling 
bodies.  Yet  when  we  ask  ourselves  the 
simplest  question  which  involves  quan- 
titative knowledge  about  gravity,  such 
as,  for  example,  Would  a  stone  and  a 
piece  of  lead  dropped  from  the  same 
point  reach  the  ground  at  the  same  time 
or  at  different  times  ?  most  of  us  are 
uncertain  as  to  the  answer.  In  fact,  it 
was  the  asking  and  the  answering  of 
this  very  question  by  Galileo,  about 
1590,  which  may  be  considered  as  the 
starting  point  of  modern  science. 

Ordinary  observation  teaches  that 
light  bodies  like  feathers  fall  slowly  and 
heavy  bodies  like  stones  fall  rapidly, 
and  up  to  Galileo's  time  it  was  taught 
in  the  schools  that  bodies  fall  with  "  velocities  proportional  to 
their  weights."  Not  content  with  book  knowledge,  however, 


FIG.  76.  Leaning  tower 
of  Pisa,  from  which  were 
performed  some  of  Gali- 
leo's famous  experiments 
on  falling  bodies 


GALILEO  (1564-1642) 

Great  Italian  physicist,  astronomer,  and  mathematician;  "founder  of  experi- 
mental science";  was  son  of  an  impoverished  nobleman  of  Pisa;  studied  medi- 
cine in  early  youth,  but  forsook  it  for  mathematics  and  science ;  was  professor 
of  mathematics  at  Pisa  and  at  Padua ;  discovered  the  laws  of  falling  bodies  and 
the  laws  of  the  pendulum ;  was  the  creator  of  the  science  of  dynamics ;  constructed 
the  first  thermometer;  first  used  the  telescope  for  astronomical  observations; 
discovered  Jupiter's  satellites  and  the  spots  on  the  sun.  Modern  physics  begins 

with  Galileo 


FALLING  BODIES 


73 


Galileo  tried  it  himself.     In  the  presence  of  the  professors 

and  students  of  the  University  of  Pisa  he  dropped  balls  of 

different  sizes  and  materials  from  the  top  of 

the  tower  of  Pisa  (Fig.  76),  180  feet  high, 

and  found  that  they  fell  in  practically  the 

same  time.    He  showed  that  even  very  light 

bodies  like  paper  fell  with  velocities  which 

approached  more  and  more  nearly  those  of 

heavy  bodies  the  more  compactly  they  were 

wadded  together.    From  these  experiments 

he  inferred  that  all  bodies,  even  the  lightest, 

would  fall  at  the  same  rate  if  it  were  not  for 

the  resistance  of  the  air. 

That  the  air  resistance  is  indeed  the  chief  factor 
in  the  slowness  of  fall  of  feathers  and  other  light 
objects  can  be  shown  by  pumping  the  air  out  of  a 
tube  containing  a  feather  (or  some  small  pieces  of 
tissue  paper)  and  a  coin  (Fig.  77).  The  more  com- 
plete the  exhaustion  the  more  nearly  do  the  feather 
and  the  coin  fall  side  by  side  when  the  tube  is  inverted.  The  air  pump, 
however,  was  not  invented  until  sixty  years  after  Galileo's  time. 

90.  Exact  proof  of  Galileo's  conclusion.  We  can  demon- 
strate the  correctness  of  Galileo's  conclusion  in  still  another 
way,  one  which  he  himself  used. 

Let  balls  of  iron  and  wood,  for  example,  be  started  together  down  the 
inclined  plane  of  Fig.  78.  They  will  be  found  to  keep  together  all  the 


C  I 

FIG  77.  Feather 
and  coin  fall  to- 
gether in  a  vacuum 


FIG.  78.    Spaces  traversed  and  velocities  acquired  by  falling  bodies  in  one, 
two,  three,  etc.  seconds 


way  down.    (If  they  roll  in  a  groove,  they  should  have  the  same  diame- 
ter ;   otherwise,  size  is  immaterial.)    The  experiment  differs  from  that 


74  FORCE  AND  MOTION 

of  the  freely  falling  bodies  only  in  that  the  resistance  of  the  air  is  here 
more  nearly  negligible  because  the  balls  are  moving  more  slowly.  In 
order  to  make  them  move  still  more  slowly  and  at  the  same  time  to 
eliminate  completely  all  possible  effects  due  to  the  friction  of  the  plane, 
let  us  follow  Galileo  and  suspend  the  different  balls  as  the  bobs  of  pen- 
dulums of  exactly  the  same  length,  two  meters  long  at  least,  and  start 
them  swinging  through  equal  arcs.  Since  now  the  bobs,  as  they  pass 
through  any  given  position,  are  merely  moving  very  slowly  down  identi- 
cal inclined  planes  (Fig.  65),  it  is  clear  that  this  is  only  a  refinement  of 
the  last  experiment.  We  shall  find  that  the  times  of  fall,  that  is,  the 
periods,  of  the  pendulums  are  exactly  the  same. 

From  the  above  experiment  we  conclude  with  Galileo  and 
with  Newton,  who  performed  it  with  the  utmost  care  a  hundred 
years  later,  that  in  a  vacuum  the  velocity  acquired  per  second 
by  a  freely  falling  body  is  exactly  the  same  for  all  bodies. 

91.  Relation  between  distance  and  time  of  fall.  Having 
found  that,  barring  air  resistance,  all  bodies  fall  in  exactly 
the  same  way,  we  shall  next  try  to  find  what  relation  exists 
between  distance  and  time  of  fall ;  and  since  a  freely  falling 
body  falls  so  rapidly  as  to  make  direct  measurements  upon 
it  difficult,  we  shall  adopt  Galileo's  plan  of  studying  the 
laws  of  falling  bodies  through  observing  the  motions  of  a 
ball  rolling  down  an  inclined  plane. 

Let  a  grooved  board  17  or  18  ft.  long  be  supported  as  in  Fig.  78,  one 
end  being  about  a  foot  above  the  other.  Let  the  side  of  the  board  be 
divided  into  feet,  and  let  the  block  B  be  set  just  16  ft.  from  the  start- 
ing point  of  the  ball  A.  Let  a  metronome  or  a  clock  beating  seconds  be 
started,  and  let  the  marble  be  released  at  the  instant  of  one  click  of  the 
metronome.  If  the  marble  does  not  hit  the  block  so  that  the  click  pro- 
duced by  the  impact  of  the  ball  coincides  exactly  with  the  fifth  click  of 
the  metronome,  alter  the  inclination  until  this  is  the  case.  (This  adjust- 
ment may  well  be  made  by  the  teacher  before  class.)  Now  start  the 
marble  again  at  some  click  of  the  metronome,  and  note  that  it  crosses 
the  1-ft.  mark  exactly  at  the  end  of  the  first  second,  the  4-ft.  mark  at 
the  end  of  the  second  second,  the  9-ft.  mark  at  the  end  of  the  third 
second,  and  hits  B  at  the  16-ft.  mark  at  the  end  of  the  fourth  second. 
This  can  be  tested  more  accurately  by  placing  B  successively  at  the 


FALLING  BODIES  75 

9-ft.,  the  4-ft.,  and  the  1-ft.  mark  and  noting  that  the  click  produced  by 
the  impact  coincides  exactly  with  the  proper  click  of  the  metronome. 

We  conclude,  then,  with  Galileo,  that,  the,  distance  traversed 
by  a  falling  body  in  any  number  of  seconds  is  the  distance 
traversed  the  first  second  times  the  square  of  the  number  of 
seconds  ;  that  is,  if  D  represents  the  distance  traversed  the  first 
second,  S  the  total  space,  and  t  the  number  of  seconds,  S  =  Dt*. 

92.  Relation  between  velocity  and  time  of  fall.  In  the  last 
paragraph  we  investigated  the  distances  traversed  in  one,  two, 
three,  etc.  seconds.  Let  us  now  investigate  the  velocities  acquired 
on  the  same  inclined  plane  in  one,  two,  three,  etc.  seconds. 

Let  a  second  grooved  board  Jlf  be  placed  at  the  bottom  of  the  incline, 
in  the  manner  shown  in  Fig.  78.  To  eliminate  friction  it  should  be 
given  a  slight  slant,  just  sufficient  to  cause  the  ball  to  roll  along  it  with 
uniform  velocity.  Let  the  ball  be  started  at  a  distance  D  up  the  incline, 
D  being  the  distance  which  in  the  last  experiment  it  was  found  to  roll 
during  the  first  second.  It  will  then  just  reach  the  bottom  of  the  incline 
at  the  instant  of  the  second  click.  Here  it  will  be  freed  from  the  influ- 
ence of  gravity,  and  will  therefore  move  along  the  lower  board  with  the 
velocity  which  it  had  at  the  end  of  the  first  second.  It  will  be  found 
that  when  the  block  is  placed  at  a  distance  exactly  equal  to  2  D  from 
the  bottom  of  the  incline,  the  ball  will  hit  it  at  the  exact  instant  of  the 
third  click  of  the  metronome,  that  is,  exactly  two  seconds  after  starting  ; 
hence  the  velocity  acquired  in  one  second  is  2  D.  If  the  ball  is  started  at 
a  distance  4  D  up  the  incline,  it  will  take  it  two  seconds  to  reach  the 
bottom,  and  it  will  roll  a  distance  4  D  in  the  next  second ;  that  is,  in 
two  seconds  it  acquires  a  velocity  4  D.  In  three  seconds  it  will  be  found 
to  acquire  a  velocity  6  Z>,  etc. 

The  experiment  shows,  first,  that  the  gain  in  velocity  each 
second  is  the  same;  second,  that  the  amount  of  this  gain 
is  numerically  equal  to  twice  the  distance  traversed  the  first 
second.  Motion,  like  the  above,  in  which  velocity  is  gained  at 
a  constant  rate  is  called  uniformly  accelerated  motion. 

In  uniformly  accelerated  motion  the  gain  each  second  in  the 
velocity  is  called  the  acceleration.  It  is  numerically  equal  to 
twice  the  distance  traversed  the  first  second. 


76 


FORCE  AND  MOTION 


93.  Formal  statement  of  the  laws  of  falling  bodies.  Put- 
ting together  the  results  of  the  last  two  paragraphs,  we  obtain 
the  folloAving  table,  in  which  D  represents  the  distance  trav- 
ersed the  first  second  in  any  uniformly  accelerated  motion. 


NUMBER  OF 

SECONDS  (t) 

VELOCITY  AT  THE 
END  OF  EACH 
SECOND  (v) 

GAIN  IN  VELOCITY 
EACH  SECOND  (a) 

TOTAL  DISTANCE 
TRAVERSED  (S) 

1 

2  D 

21) 

ID 

2 

4D 

2D 

4D 

3 

QD 

2D 

91) 

4 

SD 

2D 

16  D 

t 

2tD 

2D 

PD 

Since  D  was  shown,  in  §  92,  to  be  equal  to  one  half  of  the 
acceleration  a,  we  have  at  once,  by  substituting  J  a  for  D 
in  the  last  line  of  the  table, 

v  =  at,  (1) 

S  =  %aP.  (2) 

These  formulas  are  simply  the  algebraic  statement  of  the  facts 
brought  out  by  our  experiments,  but  the  reasons  for  these  facts  may 
be  seen  as  follows : 

Since  in  uniformly  accelerated  motion  the  acceleration  a  is  the 
velocity  in  centimeters  per  second  gained  each  second,  it  follows  at 
once  that  when  a  body  starts  from  rest,  the  velocity  which  it  has  at  the 
end  of  t  seconds  is  given  by  v  —  at.  This  is  formula  (1). 

To  obtain  formula  (2)  we  have  only  to  reflect  that  distance  traversed 
is  always  equal  to  the  average  velocity  multiplied  by  the  time.  When 
the  initial  velocity  is  zero,  as  in  this  case,  and  the  final  velocity  is  at, 
average  velocity  =  (0  +  at)  -s-  2  =  1  at.  Hence 

5  =  $  at\ 
This  is  formula  (2). 

These  are  the  fundamental  formulas  of  uniformly  accelerated  motion, 
but  it  is  sometimes  convenient  to  obtain  the  final  velocity  v  directly  from 
the  total  distance  of  fall  S,  or  vice  versa.  This  may  of  course  be  done 

by  simply  substituting  in  (2)  the  value  of  t  obtained  from  (1),  namely,  -• 
This  gives 

v  =  V2  a5.  (3) 


FALLING  BODIES 


77 


Distances 
in  ft.  per  sec.  in  feet 

Ot 


To  illustrate  the  use  of  these  formulas,  sup- 
pose we  wish  to  know  with  what  velocity  a 
body  will  hit  the  earth  if  it  falls  from  a  height 
of  200  meters,  or  20,000  centimeters.  From  (6) 
we  get 


v  -  V2  x  980  x  20,000  =  6261  cm.  per  second. 

95.  Height  of  ascent.  If  we  wish  to  find  the 
height  S  to  which  a  body  projected  vertically 
upward  will  rise,  we  reflect  that  the  time  of 
ascent  must  be  the  initial  velocity  divided  by 
the  upward  velocity  which  the  body  loses  per 

second,  that  is,  t  =  - ;  and  the  height  reached 
9 


32.16 « 


94.  Acceleration  of  a  freely  falling  body.  If  in  the  above 
experiment  the  slope  of  the  plane  be  made  steeper,  the  results 
will  obviously  be  precisely  the  same,  ex-  velocities 
cept  that  the  acceleration  has  a  larger 
value.  If  the  board  is  tilted  until  it  be- 
comes vertical,  the  body  becomes  a  freely 
falling  body  (Fig.  79).  In  this  case  the 
distance  traversed  the  first  second  is 
found  to  be  490  centimeters,  or  16.08 
feet.  Hence  the  acceleration,  expressed 
in  centimeters,  is  980 ;  in  feet,  32.16. 
This  acceleration  of  free  fall,  called  the 
acceleration  of  gravity,  is  usually  denoted 
by  the  letter  g.  For  freely  falling  bodies, 
then,  the  three  formulas  of  the  preceding 
paragraph  become 

v  =  fft,  (4) 


64.32 


128.64 


0 

(16.08) 
16.08 


>  (48.24) 


64.32 


(80.40) 


144.72 


(112.56) 


257.28 


FIG.  79.    A  freely  fall- 
ing body 


78 


FOKCE  AND  MOTION 


must  be  this  multiplied  by  the  average  velocity ;  that  is, 


(7) 


FIG.  80.    Path  of  a  projectile 


Since  (7)  is  the  same  as  (6),  we  learn  that  in  a  vacuum  the  speed  with 
which  a  body  must  be  projected  upward  to  rise  to  a  given  height  is  the 
same  as  the  speed  which  it  acquires  in  falling  from  the 
same  height. 

96.  Path   of   a   projectile.     Imagine   a   projectile 
to  be  shot  along  the  line  ab  (Fig.  80).    If  it 
were  not  for  gravity  and  the  resistance  of 

the  air,  the  projectile  would   travel 
with  uniform  velocity  along  the 
line  ab,  arriving  at  the  points 
1,    2,    3,  etc.   at   the   end 
of  the  successive  seconds. 
Because  of  gravity,  how- 
ever, the  projectile  would 
be  vertically  below  these 
points    by    the    distances 

16.08  ft.,  64.32  ft.,  144.72  ft.,  etc.  Hence  it  would  follow  the  path  indi- 
cated by  the  dotted  curve  (a  parabola).  But  because  of  air  resistance 
the  height  of  flight  and  range  are  diminished,  and  the  general  shape  of 
the  trajectory  is  similar  to  the  continuous  curved  line. 

97.  The  airplane.    The  principles  underlying  stability,  as 
well  as  those  having  to  do  with  the  resolution  of  forces,  are 
well  illustrated  by  the  modern  airplane,  which  grew  out  of  a 
study  of  the  laivs  of  air  resistance  and  the  properties  of  gliders. 

When  a  plate  of  area  A  moves  in  still  air  in  a  direction 
perpendicular  to  its  plane,  with  a  velocity  V  (see  Fig.  81,  (1)), 
the  air  resistance  R  is  found  by  experiment  to  be  given  by 
the  equation 

R  =  KAY*,  (8) 

where  R  is  the  force  in  kilograms,  A  the  area  in  square  meters, 
V  the  speed  in  meters  per  second,  and  K  a  constant  which  has 
the  value  .08.  Thus,  when  an  automobile  is  going  40  miles 


FALLING  BODIES 


79 


per  hour  (18  meters  per  second),  the  force  of  the  air  against 
.5  square  meter  of  wind-shield  is  .08  x  .5  x  (18)2=  13  kg. 
When  the  plate  moves  so  that  the  direction  of  its  motion 
makes  a  small  angle  i  (between  0°  and  10°)  (Fig.  81,  (2)) 
with  its  plane,  the  air  resistance  R  is  perpendicular  to  the 
plate  and  is  given  by  the  empirical  formula 

R  =  kAV%  (9) 

where  J?,  A,  and  V  have  the  same  significance  as  above,  i  is 
the  angle  in  degrees,  and  k  is  very  near  to  .005. 

As  i,  which  is  called  the  angle  of  attack  or  of  incidence, 
decreases,   the  center  of   pressure   C  (Fig.  81,  (2))    moves 

R 


(1) 


FIG.  81.    Forces  acting  on  a  glider 


toward  the  front  edge  and  tends  toward  a  certain  definite 
limiting  position  CQ  as  the  angle  i  becomes  smaller  and  smaller. 
When  a  flat  object  like  a  sheet  of  paper  is  allowed  to  fall, 
it  is  acted  upon  by  two  forces,  one  W,  acting  at  its  center 
of  gravity  g,  which  is  always  vertical  and  equal  to  the 
weight,  and  the  other  R,  which  is  due  to  the  air  resistance 
acting  at  the  center  of  pressure  C  and  perpendicular  to  the 
plane.  If  the  plane  is  to  fall  without  acceleration  and  with- 
out rotation,  that  is,  if  it  is  to  glide,  it  is  clear  that  these 
two  forces  must  act  at  the  same  point  and  be  equal  and 
opposite.  Hence  any  gliding  plane  must  be  horizontal  and 
must  move  with  a  speed  V  at  an  angle  i  (see  Fig.  81  (3)), 
given  by  the  equation 

(10) 


80 


FORCE  AND  MOTION 


Since  the  plane  must  be  horizontal,  and  since  there  is 
only  one  angle  of  attack  which  will  bring  the  center  of 
pressure  and  the  center  of  gravity  together,  it  will  be  seen 
that  the  gliding  angle  i  is  the 
same  for  all  values  of  the  weight 
W,  but  that  the  speed  V  will  be 
proportional  to  the  square  root 
of  the  weight  (see  equation  10).  FIG.  82.  A  stabilized  glider 

The  foregoing  theory  of  gliding  may  be  nicely  illustrated  with  paper 
gliders  thus :  Fold  a  sheet  of  writing  paper  lengthwise,  exactly  along 
the  middle.  Refold  the  upper  half  twice  on  itself  so  as  to  make  it  \  its 
original  width;  then  fasten  it  down  to  the  lower  half  with  paste  or 
light  gummed  paper.  The  center  of  gravity  will  now  be  -^  of  the  new 
width  behind  the  back  edge  of  the  folded 
portion.  When  started  slowly  with  the 
folded  edge  forward,  the  paper  will  glide 
as  described.  Heavier  paper  will  glide  at 
the  same  angle  but  with  greater  speed. 
If  started  thin  edge  foremost,  the  forces 
at  once  turn  the  glider  over,  and  it  glides 
with  the  heavier  edge  in  front.  To  in- 
crease the  lateral  stability  it  is  sufficient 
to  give  the  paper  the  shape  shown  in 
Fig.  82.  (See  opposite  p.  317.) 

When  the  motor  of  an  airplane 
stops,  the  plane   glides  safely  to    FlG>  83.  Forces  acting  on  an 
earth  under  the  laws  of  equation  airplane  in  flight 

10.     If  the  airplane   propeller  is 

pulling  forward  with  a  horizontal  force  Q,  and  the  wings  are 
set  back  at  an  angle  i,  R  and  W  no  longer  balance  each  other, 
but  their  resultant  is  equal  and  opposite  to  Q;  that  is,  the 
forces  R,  W,  and  Q  form,  a  system  in  equilibrium,  as  shown 
in  Fig.  83.  The  plane  moves  forward  horizontally  with  a 
speed  V.  If  the  angle  i  or  the  force  Q  is  increased,  the  plane 
rises ;  if  i  or  Q  is  diminished,  the  plane  descends. 


FALLING  BODIES  81 

98.  The  laws  of  the  pendulum.  The  first  law  of  the  pendu- 
lum was  found  in  §  90,  namely, 

(1)  The  periods  of  pendulums  of  equal  lengths  swinging  through 
short  arcs  are  independent  of  the  weight  and  material  of  the  bobs. 

Let  the  two  pendulums  of  §  90  be  set  swinging  through  arcs  of 
lengths  5  centimeters  and  25  centimeters  respectively.  We  shall  thus 
find  the  second  law  of  the  pendulum,  namely, 

(2)  The  period  of  a  pendulum  swinging  through  a  short  arc  is 
independent  of  the  amplitude  of  the  arc. 

Let  pendulums  ^  and  ^  as  long  as  the  above  be  swung  with  it.  The 
long  pendulum  will  be  found  to  make  only  one  vibration  while  the  others 
are  making  two  and  three  respectively.  The  third  law  of  the  pendulum 
is  therefore 

(3)  The  periods  of  pendulums  are  directly  proportional  to  the 
square  roots  of  their  lengths. 

The  accurate  determination  of  g  is  never  made  by  direct  measure- 
ment, for  the  laws  of  the  pendulum  just  established  make  this  instru- 
ment by  far  the  most  accurate  one  obtainable  for  this  determination. 
It  is  only  necessary  to  measure  the  length  of  a  long  pendulum  and  the 
time  t  between  two  successive  passages  of  the  bob  across  the  mid-point, 

and  then  to  substitute  in  the  formula  t  =  *\l-  in  order  to  obtain  g  with  a 

iff 

high  degree  of  precision.  The  deduction  of  this  formula  is  not  suitable 
for  an  elementary  text,  but  the  formula  itself  may  well  be  used  for 
checking  the  value  of  g,  given  in  §  94. 

QUESTIONS  AND  PROBLEMS 

1.  If  a  body  starts  from  rest  and  travels  with  a  constant  acceleration 
of  10  ft.  per  second  each  second,  how  fast  will  it  be  going  at  the  close 
of  the  fifth  second?  What  is  its  average  velocity  during  the  5  sec.,  and 
how  far  did  it  go  in  this  time? 

2.  A  body  starting  from  rest  and  moving  with  uniformly  accelerated 
motion  acquired  a  velocity  of  60  ft.  per  second  in  5  sec.   Find  the  acceler- 
ation.   What  distance  did  it  traverse  during  the  first  second  ?  the  fifth  ? 

3.  A  body  moving  with  uniformly  accelerated  motion  traversed  6  ft. 
during  the  first  second.  Find  the  velocity  at  the  end  of  the  fourth  second. 


82 


FORCE  AND  MOTION 


4.  A  ball  thrown  across  the  ice  started  with  a  velocity  of  80  ft. 
per  second.    It  was  retarded  by  friction  at  the  rate  of  2  ft.  per  second 
each  second.    How  long  did  it  roll?    How  far  did 

it  roll  ? 

5.  A  bullet  was  fired  with  a  velocity  of  2400  ft.  per 
second  from  a  rifle  having  a  barrel  2  ft.  long.    Find 
(a)  the  average  velocity  of  the  bullet  while  moving 
the  length  of  the  barrel;   (b)  the  time  required  to 
move  through  the  barrel ;  (c)  the  acceleration  of  the 
bullet  while  in  the  barrel. 

6.  A  ball  was  thrown  vertically  into  the  air  with 
a  velocity  of  160  ft.  per  second.    How  long  did  it  re- 
main in  the  air?    (Take  g=32  ft.  per  sec2.) 

7.  A  baseball  was  thrown  upward.    It  remained 
in  the  air  6  sec.    With  what  velocity  did  it  leave  the 
hand  ?    How  high  did  it  go  ? 

8.  A  ball  dropped  from  the  top  of  the  Woolworth 
Building  in  New  York  City,  780  ft.  above  Broadway, 
would  require  how  many  seconds  to  fall  ?  With  what 
velocity  would  it  strike  ?    (Take  g  =  32  ft.  per  sec2.) 

9.  How  high  was  an  airplane  from  which  a  bomb 
fell  to  earth  in  10  sec.  ? 

10.  WTith  what  speed  does  a  bullet  strike  the  earth 
if  it  is  dropped  from  the  Eiffel  Tower,  335  m.  high  ? 

11.  If  the  acceleration  of  a  marble  rolling  down 
an  inclined  plane  is  20  cm.  per  second,  what  velocity 
will  it  have  at  the  bottom,  the  plane  being  7  m.  long  ? 

12.  If  a  man  can  jump  3  ft.  high  on  the  earth,  how 
high  could  he  jump  on  the  moon,  where  g  isj  as  much? 

13.  The  brakes  were  set  on  a  train  running  60  mi.  per  hour,  and  the 
train  stopped  in  20  sec.    Find  the  acceleration  in  feet  per  second  each 
second  and  the  distance  the  train  ran  after  the  brakes  were  applied. 

14.  How  far  will  a  body  fall  from  rest  during  the  first  half  second  ? 

15.  With  what  velocity  must  a  ball  be  shot  upward  to  rise  to  the 
height  of  the  Washington  Monument  (555  ft.)?    How  long  before  it 
will  return  ? 

16.  Fig.  84  represents  the  pendulum  and  escapement  of  a  clock. 
The  escapement  wheel  D  is  urged  in  the  direction  of  the  arrow  by  the 
clock  weights  or  spring.    The  slight  pushes  communicated  by  the  teeth 
of  the  wheel  keep  the  pendulum  from  dying  down.    Show  how  the 
length  of  the  pendulum  controls  the  rate  of  the  clock. 

17.  What  force  supports  an  airplane  in  flight?  What  is  "gliding"? 


FIG.  84 


NEWTON'S  LAWS  OF  MOTION  83 

18.  A  pendulum  that  makes  a  single  swing  per  second  in  New 
York  City  is  99.3  cm.,  or  39.1  in.,  long.  Account  for  the  fact  that  a 
seconds  pendulum  at  the  equator  is  39  in.  long,  while  at  the  poles  it  is 
39.2  in.  long. 

19.  How  long  is  a  pendulum  whose  period  is  3  sec.?    2  sec.?    \  sec.? 
£sec.? 

20.  A  man  was  let  down  over  a  cliff  on  a  rope  to  a  depth  of  500  ft. 
What  was  his  period  as  a  pendulum  ? 


NEWTON'S  LAWS  OF  MOTION 

99.  First  law  —  inertia.  It  is  a  matter  of  everyday  observa- 
tion that  bodies  in  a  moving  train  tend  to  move  toward  the 
forward  end  when  the  train  stops  and  toward  the  rear  end 
when  the  train  starts ;  that  is,  bodies  in  motion  seem  to  want 
to  keep  on  moving,  and  bodies  at  rest  to  remain  at  rest. 

Again,  a  block  will  go  farther  when  driven  with  a  given 
blow  along  a  surface  of  glare  ice  than  when  knocked  along 
an  asphalt  pavement.  The  reason  which  everyone  will  assign 
for  this  is  that  there  is  more  friction  between  the  block  and 
the  asphalt  than  between  the  block  and  the  ice.  But  when 
would  the  body  stop  if  there  were  no  friction  at  all? 

Astronomical  observations  furnish  the  most  convincing 
answer  to  this  question^  for  we  cannot  detect  any  retardation 
at  all  in  the  motions  of  the  planets  as  they  swing  around  the 
sun  through  empty  space. 

Furthermore,  since  mud  flies  off  tangentially  from  a  rotating 
carriage  wheel,  or  water  from  a  whirling  grindstone,  and  since, 
too,  we  have  to  lean  inward  to  prevent  ourselves  from  falling 
outward  in  going  around  a  curve,  it  appears  that  bodies  in 
motion  tend  to  maintain  not  only  the  amount  but  also  the 
direction  of  their  motion  (see  gyrocompass  opposite  p.  223). 

In  view  of  observations  of  this  sort  Sir  Isaac  Newton,  in 
1686,  formulated  the  following  statement  and  called  it  the 
first  law  of  motion. 


84  FOKCE  AND  MOTION 

Every  body  continues  in  its  state  of  rest  or  uniform  motion  in  a 
straight  line  unless  impelled  by  external  force  to  change  that  state. 

This  property,  which  all  matter  possesses,  of  resisting  any  at- 
tempt to  start  it  if  at  rest,  to  stop  it  if  in  motion,  or  in  any  way  to 
change  either  the  direction  or  amount  of  its  motion,  is  called  inertia. 

100.  Centrifugal  force.    It  is  inertia  alone  Xyhich  prevents 
the  planets  from  falling  into  the  sun,  which  causes  a  rotating 
sling  to  pull  hard  on  the  hand  until  the  stone  is  released, 
and  which  then  causes  the  stone  to  fly  off   tangentially.    It 
is  inertia  which  makes  rotating 

liquids  move  out  as  far  as  possi- 
ble from  the  axis  of  rotation 
(Fig.  85),  which  makes  flywheels 
sometimes  burst,  which  makes 
the  equatorial  diameter  of  the 
earth  greater  than  the  polar, 

which  makes  the  heavier  milk 

,  ,.     , !        ,,         ,,      ,.   ,  .  FIG.  85.    Illustrating  centrifugal 

move  out  farther  than  the  lighter  f orce 

cream  in  the  dairy  separator  (see 

opposite  p.  85),  etc.  Inertia  manifesting  itself  in  this  tendency 
of  the,  parts  of  rotating  systems  to  move  away  from  the  center  of 
rotation  is  called  centrifugal  force. 

101.  Momentum.    The  quantity  of  motion  possessed  by  a 
moving  body  is  defined  as  the  product  of  the  mass  and  the 
velocity  of  the  body.    It  is  commonly  called  momentum.    Thus, 
a  10-gram  bullet  moving  50,000  centimeters  per  second  has 
500,000  units  of  momentum ;  a  1000-kg.  pile  driver  moving 
1000  centimeters  per  second  has  1,000,000,000  units  of  mo- 
mentum ;  etc.    We  shall  always  express  momentum  hi  C.G.S. 
units,  that  is,  as  a  product  of  grams  by  centimeters  per  second. 

102.  Second  law.     Since  a  2-gram  mass  is  pulled  toward 
the  earth  with  twice  as  much  force  as  is  a  1-gram  mass,  and 
since  both,  when  allowed  to  fall,  acquire  the  same  velo'city  in 


SIR  ISAAC  NEWTON  (1642-1727) 

English  mathematician  and  physicist,  "prince  of  philosophers"  ; 
professor  of  mathematics  at  Cambridge  University;  formulated 
the  law  of  gravitation ;  discovered  the  binomial  theorem ;  invented 
the  method  of  the  calculus ;  announced  the  three  laws  of  motion 
which  have  become  the  basis  of  the  science  of  mechanics ;  made 
important  discoveries  in  light;  is  the  author  of  the  celebrated 
"  Principia  "  (Principles  of  Natural  Philosophy) ,  published  in  1687 


Skim-milk  Outlet 


Cream  Outlet 
Skim-milk  Outlet 


THE  CREAM  SEPARATOR  (2) 

The  milk  is  poured  into  a  central  tube  (see  1,  a)  at  the  top  of  a  nest  of  disks  (see 
1  and  4}  situated  within  a  steel  bowl.  The  milk  passes  to  the  bottom  of  the  cen- 
tral tube,  then  rises  through  three  series  of  holes  (see  1,  b,  b,  b,  etc.)  in  the  nest 
of  disks,  and  spreads  outward  into  thin  sheets  between  the  slightly  separated 
disks.  By  means  of  a  system  of  gears  (see  3)  the  disks  and  bowl  are  made  to 
revolve  from  6000  to  8000  revolutions  per  minute.  The  separation  of  cream  from 
skim-milk  is  quickly  effected  in  these  thin  sheets ;  the  heavier  skim-milk  (water, 
casein,  and  sugar)  is  thrown  outward  by  centrifugal  force  against  the  under  sur- 
faces of  the  bowl  disks  (see  5),  then  passes  downward  and  outward  along  these 
under  surfaces  to  the  periphery  of  the  bowl  (see  1,  d,  d,  d,  etc.),  and  finally  rises 
to  the  skim-milk  outlet.  The  lighter  cream  is  thereby  at  the  same  time  displaced 
inward  and  upward  along  the  upper  surfaces  of  the  bowl  disks  (see  5),  then  passes 
over  the  inner  edges  of  the  disks  to  slots  (see  1,  c,  c,  c,  etc.)  on  the  outside  of  the 
central  tube,  finally  rising  to  the  cream  outlet,  which  is  above  the  outlet  for  the 
skim-milk  (see  1  and  2) 


NEWTON'S  LA\VS  OF  MOTION  85 

a  second,  it  follows  that  in  this  case  the  momentums  produced 
in  the  two  bodies  by  the  two  forces  are  exactly  proportional  to 
the  forces  themselves.  In  all  cases  in  which  forces  simply  over- 
come inertias  this  rule  is  found  to  hold.  Thus,  a  3000-pound 
pull  on  an  automobile  on  a  level  road,  where  friction  may  be 
neglected,  imparts  in  a  second  just  twice  as  much  velocity  as 
does  a  1500-pound  pull.  In  view  of  this  relation  Newton's 
second  law  of  motion  was  stated  thus:  Rate  of  change  of 
momentum  is  proportional  to  the  force  acting,  and  the  change 
takes  place  in  the  direction  in  which  the  force  acts. 

103.  The  third  law.  When  a  man  jumps  from  a  boat  to 
the  shore,  we  all  know  that  the  boat  experiences  a  backward 
thrust ;  when  a  bullet  is  shot  from  a  gun,  the  gun  recoils,  or 
"  kicks  " ;  when  a  billiard  ball  strikes  another,  it  loses  speed, 
that  is,  is  pushed  back  while  the  second 
ball  is  pushed  forward.  The  following 
experiment  will  show  how  effects  of 
this  sort  may  be  studied  quantitatively. 

Let  a  sceel  ball  A  (Fig.  80)  be  allowed 
to  fall  from  a  position  C  against  another 
exactly  similar  ball  B.  In  the  impact  A  will 
lose  practically  all  of  its  velocity,  and  B  will  ^  ^ 

move  to  a  position  D,  which  is  at  the  same        FIG.  86.   Illustration  of 
height  as   C.    Hence  the  velocity  acquired  third  law 

by  B  is  almost  exactly  equal  to  that  which 

A  had  before  impact.  These  velocities  would  be  exactly  equal  if  the 
balls  were  perfectly  elastic.  It  is  found  to  be  true  experimentally  that 
the  momentum  acquired  by  B  plus  that  retained  by  A  is  exactly  equal 
to  the  momentum  which  A  had  before  the  impact.  The  momentum 
acquired  by  B  is  therefore  exactly  equal  to  that  lost  by  A.  Since,  by  the 
second  law,  change  in  momentum  is  proportional  to  the  force  acting, 
this  experiment  shows  that  A  pushed  forward  on  B  with  precisely  the 
same  force  with  which  B  pushed  back  on  A. 

Now  the  essence  of  Newton's  third  law  is  the  assertion 
that  in  the  case  of  the  man  jumping  from  the  boat  the  mass 


86  FORCE  AND  MOTION 

of  the  man  times  his  velocity  is  equal  to  the  mass  of  the 
boat  times  its  velocity,  and  that  in  the  case  of  the  bullet  and 
gun  the  mass  of  the  bullet  times  its  velocity  is  equal  to  the 
mass  of  the  gun  times  its  velocity.  The  truth  of  this  assertion 
has  been  established  by  a  great  variety  of  experiments. 

Newton  stated  his  third  law  thus:  To  every  action  there  is 
an  equal  and  opposite  reaction. 

Since  force  is  measured  by  the  rate  at  which  momentum 
changes,  this  is  only  another  way  of  saying  that  whenever  a 
body  acquires  momentum  some  other  body  acquires  an  equal  and 
opposite  momentum. 

It  is  not  always  easy  to  see  at  first  that  setting  one  body 
into  motion  involves  imparting  an  equal  and  opposite  momen- 
tum to  another  body.  For  example,  when  a  gun  is  held 
against  the  earth  and  a  bullet  shot  upward,  we  are  conscious 
only  of  the  motion  of  the  bullet;  the  other  body  is  in  this 
case  the  earth,  and  its  momentum  is  the  same  as  that  of  the 
bullet.  On  account  of  the  greatness  of  the  earth's  mass, 
however,  its  velocity  is  infinitesimal. 

104.  The  dyne.  Since  the  gram  of  force  varies  somewhat  with  locality, 
it  has  been  found  convenient  for  scientific  purposes  to  take  the  second 
law  as  the  basis  for  the  definition  of  a  new  unit  of  force.  It  is  called  an 
absolute,  or  C.G.S.,  unit  because  it  is  based  upon  the  fundamental  units 
of  length,  mass,  and  time,  and  is  therefore  independent  of  gravity.    It 
is  named  the  dyne  and  is  defined  as  the  force  which,  acting  for  one  second 
upon  any  mass,  imparts  to  it  one  unit  of  momentum  ;  or  the  force  which,  act- 
ing for  one  second  upon  a  one-gram  mass,  produces  a  change  in  its  velocity 
of  one  centimeter  per  second. 

105.  A  gram  of  force  equivalent  to  980  dynes.    A  gram  of  force  was 
defined  as  the  pull  of  the  earth  upon  1  gram  of  mass.    Since  this  pull  is 
capable  of  imparting  to  this  mass  in  1  second  a  velocity  of  980  centi- 
meters per  second,  that  is,  980  units  of  momentum,  and  since  a  dyne 
is  the  force  required  to  impart  in  1  second  1  unit  of  momentum,  it  is 
clear  that  the  gram  of  force  is  equivalent  to  980  dynes  of  force.    The 
dyne  is  therefore  a  very  small  unit,  about  equal  to  the  force  with  which 
the  earth  attracts  a  cubic  millimeter  of  water. 


NEWTON'S  LAWS  OF  MOTION  87 

106.  Algebraic  statement  of  the  second  law.  If  a  force  F  acts  for  t 
seconds  on  a  mass  of  m  grams,  and  in  so  doing  increases  its  velocity 
v-  centimeters  per  second,  then,  since  the  total  momentum  imparted  in 

a  time  t  is  mv,  the  momentum  imparted  per  second  is  —  ;  and  since 
force  in  dynes  is  equal  to  momentum  imparted  per  second,  we  have 


But  since  -  is  the  velocity  gained  per  second,  it  is  equal  to  the  acceler- 
ation a.  Equation  (8)  may  therefore  be  written 

F  =  ma.  (9) 

This  is  merely  stating  in  the  form  of  an  equation  that  force  is 
measured  by  rate  of  change  of  momentum.  Thus,  if  ap  engine,  after  pull- 
ing for  30  sec.  on  a  train  having  a  mass  of  2,000,000  kg.,  has  given  it  a 
velocity  of  60  cm.  per  second,  the  force  of  the  pull  is  2,000,000,000  x  |£  = 
4,000,000,000  dynes.  To  reduce  this  force  to  grams  we'  divide  by  980, 
and  to  reduce  it  to  kilos  we  divide  further  by  1000.  Hence  the  pull 
exerted  by  the  engine  on  the  train  =  4'0Sgo°tggo000  =  4081  kS'->  or  4-08l 
metric  tons. 

QUESTIONS  AND  PROBLEMS 

1.  What  principle   is  applied  when  one   tightens  the    head  of  a 
hammer  by  pounding  on  the  handle? 

2.  Why  does  not  the  car  C  of  Fig.  87  fall?  What  carries  it  from  BtoDl 

3.  Why  does  a  flywheel  cause  machinery  to  run  more   steadily? 

4.  Balance  a  calling  card  on  the  finger  and  place  a  coin  upon  it. 
Snap  out  the  card,  leaving  the 

coin   balanced  on  the  finger. 
What  principle  is  illustrated? 

5.  Is  it  any  easier  to  walk 
toward  the  rear  than  toward 

the  front  of  a  rapidly  moving  B 

train?  Why?  Fl(.    87     A  very  ancient  loop  the  loops 

6.  Suspend  a  weight  by  a 

string.  Attach  a  piece  of  the  same  string  to  the  bottom  of  the  weight. 
If  the  lower  string  is  pulled  with  a  sudden  jerk,  it  breaks  ;  but  if  the 
pull  is  steady,  the  upper  string  will  break.  Explain. 

7.  Where  does  a  body  weigh  the  more,  at  the  poles  or  at  the  equator  ? 
Give  two  reasons. 


88 


FORCE  AND  MOTION 


8.  If  the  trains    A,  B,  and  C  (Fig.  88)  are  all  running  60  mi. 
per  hour,  what  is  the  velocity  of  A   with  reference  to  5?   to  C? 

9.  If  a  weight  is  dropped  from  the  roof  to  the  floor  of  a  moving- 
car,  will  it  strike  the  point  on  the  floor  which  was  di- 
rectly beneath  its  starting  point? 

10.  Why  is  a  running  track  banked  at  the  turns?  C< 

11.  If  the  earth  were  to  cease  rotating,  would  bodies         pIG-  g8 
on  the  equator  weigh  more  or  less  than  now  ?   Why  ? 

12.  How  is  the   third   law  involved   in   rotary  lawn  sprinklers? 

13.  The  modern  way  of  drying  clothes  is  to  place  them  in  a  large 
cylinder  with  holes  iu  the  sides,  and  then  to 

set  it  in  rapid  rotation.    Explain. 

14.  Explain  how  reaction  pushes  the  ocean 
liner  and  the  airplane  forward. 

15.  If  one  ball  is  thrown  horizontally  from 
the  top  of  a  tower  and  another  dropped  at  the 
same  instant,  which  will  strike  the  earth  first  ? 
(Remember  that  the  acceleration  produced  by 
a  force  is  in  the  direction  in  which  the  force 
acts  and  proportional  to  it,  whether  the  body 
is  at  rest  or  in  motion.    See  second  law.)    If 

possible,  try  the  experiment  with  an  arrangement  like  that  of  Fig.  89- 

16.  If  a  rifle  bullet  were  fired  horizontally  from  a  tower  19.6  m.  high 
with  a  speed  of  300  m.,  how  far  from  the  base  of  the  tower  would  it 
strike  the  earth  if  there  were  no  air  resistance  ? 


\ 


FIG.  89.  Illustrating  New- 
ton's second  law 


FIG.  90.  Hydraulic  ram 

17.  The  hydraulic  ram  (Fig.  90)  is  a  practical  illustration  of  the 
principle  of  inertia.    With  its  aid  water  from  a  pond  P  can  be  raised 


NEWTON'S  LAWS  OF  MOTION 


FIG.  91 


into  a  tank  that  stands  at  a  higher  level  than  the  pond.  With  the  aid 
of  Fig.  91  explain  how  it  works,  remembering  that  the  valve  V  will  not 
close  until  the  stream  of  water 
flowing  around  it  acquires  suffi- 
cient speed. 

18.  If  two  men  were  together 
in  the  middle  of  a  perfectly  smooth 
(frictionless)    pond    of  ice,    how 
could  they  get  off?    Could  one 
man    get   off   if   he   were    there 
alone  ? 

19.  If  a  10-g.  bullet  is  shot  from  a  5-kg.  gun  with  a  speed  of  400  m. 
per  second,  what  is  the  backward  speed  of  the  gun  ? 

20.  If  a  team  of  horses  pulls  500  Ib.  in  drawing  a  wagon,  with  what 
force  does  the  wagon  pull  backward  upon  the  team  ?  ^hy  do  the  wheels 
turn  before  the  hoofs  of  the  horses  slide  ? 

21.  Why  does  a  falling  mass,  on  striking,  exert  a  force  in  excess  of 
its  weight? 

22.  A  pull  of  a  dyne  acts  for  3  sec.  on  a  mass  of  1  g.    What  velocity 
does  it  impart  ? 

23.  How  long  must  a  force  of  100  dynes  act  on  a  mass  of  20  g.  to 
impart  to  it  a  velocity  of  40  cm.  per  second? 

24.  A  force  of  1  dyne  acts  on  1  g.  for  1  sec.    How  far  has  the  gram 
been  moved  at  the  end  of  the  second  ? 

A  laboratory  exercise  on  the  composition  of  forces  should  be  performed 
during  the  study  of  this  chapter,  See,  for  example,  Experiment  11  of  the 
authors'  Manual. 


CHAPTER  VI 

MOLECULAR  FORCES* 
MOLECULAR  FORCES  IN  SOLIDS.    ELASTICITY 

107.  That  the  molecules  of  solids  cling  together  with  forces 
of  great  magnitude  is  proved  by  some  of  the  simplest  facts  of 
nature ;  for  solids  not  only  do  not  expand  indefinitely 
like  gases,  but  it  often  requires  enormous  forces  to 
pull  their  molecules  apart.  Thus,  a  rod  of  cast  steel 
1  centimeter  in  diameter  may  be  loaded  with  a  weight 
of  7.8  tons  before  it  will  be  pulled  in  two. 

The  following  are  the  weights  in  kilograms  necessary 
to  break  drawn  wires  of  different  materials,  1  square 
millimeter  in  cross  section, —  the  so-called  relative 
tenacities  of  the  wires. 

Lead,  2.6  Platinum,  43  Iron,  77 

Silver,  37  Copper,  51  Steel,  91 

108.  Elasticity.  We  can  obtain  additional  infor- 
mation about  the  molecular  forces  existing  in  different 
substances  by  studying  what 
happens  when  the  weights  ap- 
plied are  not  large  enough  to 
break  the  wires. 


Thus,  let  a  long  steel  wire  (for  ex- 
P  ample,  No.  26  piano  wire)  be  suspended 

FIG.  92.  Elasticity  of  a  steel  wire      from  a  hook  in  the  ceiling,  and  let  the 

*  This  chapter  should  be  preceded  by  a  laboratory  experiment  in  which 
Hooke's  law  is  discovered  by  the  pupil  for  certain  kinds  of  deformation 
easily  measured  in  the  laboratory.  See,  for  example,  Experiment  13  of  the 
authors'  Manual. 

90 


MOLECULAR  FORCES  IN  SOLIDS  91 

lower  end  be  wrapped  tightly  about  one  end  of  a  meter  stick,  as  in 
Fig.  92.  Let  a  fulcrum  c  be  placed  in  a  notch  in  the  stick  at  a  distance 
of  about  5  cm.  from  the  point  of  attachment  to  the  wire,  and  let  the 
other  end  of  the  stick  be  provided  with  a  knitting  needle,  one  end  of 
which  is  opposite  the  vertical  mirror  scale  S.  Let  enough  weights  be 
applied  to  the  pan  P  to  place  the  wire  under  slight  tension ;  then  let 
the  reading  of  the  pointer  p  on  the  scale  S  be  taken.  Let  three  or  four 
kilogram  weights  be  added  successively  to  the  pan  and  the  correspond- 
ing positions  of  the  pointer  read.  Then  let  the  readings  be  taken  again  as 
the  weights  are  successively  removed.  In  this  last  operation  the  pointer 
will  probably  be  found  to  come  back  exactly  to  its  first  position. 

This  characteristic  which  the  steel  has  shown  in  this  experi- 
ment, of  returning  to  its  original  length  when  the  stretching 
weights  are  removed,  is  an  illustration  of  a  property  possessed 
to  a  greater  or  less  extent  by  all  solid  bodies.  It  is  called 
elasticity. 

109.  Limits  of  perfect  elasticity.    If  a  sufficiently   large 
weight  is  applied  to  the  end  of  the  wire  of  Fig.  92,  it  will  be 
found  that  the  pointer  does  not  return  exactly  to  its  original 
position  when  the  weight  is  removed.     We  say,  therefore, 
that  steel  is  perfectly  elastic  only  so  long  as  the  distorting 
forces   are  kept  within  certain  limits,  and  that  as  soon  as 
these    limits    are    overstepped    it   no    longer   shows    perfect 
elasticity.     Different   substances   differ  very  greatly   in  the 
amount  of   distortion   which  they   can   sustain  before   they 
show  this  failure  to  return  completely  to  the  original  shape. 

110.  Hooke's  law.    If  we  examine  the  stretches  produced  by 
the  successive  addition  of  kilogram  weights  in  the  experiment 
of  §  108,  Fig.  92,  we  shall  find  that  these  stretches  are  all 
equal,  at  least  within  the  limits  of  observational  error.    Very 
carefully  conducted  experiments  have  shown  that  this  law, 
namely,  that  the  successive  application  of  equal  forces  pro- 
duces a  succession  of  equal  stretches,  holds  very  exactly  for 
all  sorts  of  elastic  displacements  so  long,  and  only  so  long, 
as  the  limits  of  perfect  elasticity  are  not  overstepped.    This 


92  MOLECULAR  FORCES 

law  is  known  as  Hooke's  law,  after  the  Englishman  Robert 
Hooke  (1635-1703).  Another  way  of  stating  this  law  is  the 
folloAving  :  Within  the  limits  of  perfect  elasticity  elastic  deforma- 
tions of  any  sort,  be  they  twists  or  bends  or  stretches,  are  directly 
proportional  to  the  forces  producing  them.  The  common  spring 
balance  (Fig.  57)  is  an  application  of  Hooke's  law. 

111.  Cohesion   and  adhesion.    The  preceding  experiments 
have  brought  out  the  fact  that,  in  the  solid  condition  at  least, 
molecules  of  the  same  kind  exert  attractive  forces  upon  one 
another.    That   molecules   of    unlike   substances   also   exert 
mutually  attractive  forces  is  equally  true,  as  is  proved  by 
the  fact  that  glue  sticks  to  wood  with  tremendous  tenacity, 
mortar  to  bricks,  nickel  plating  to  iron,  etc. 

The  forces  which  bind  like  kinds  of  molecules  together  are 
commonly  called  cohesive  forces ;  those  which  bind  together 
molecules  of.  unlike  kind  are  called  adhesive  forces.  Thus,  we 
say  that  mucilage  sticks  to  wood  because  of  adhesion,  while 
wood  itself  holds  together  because  of  cohesion.  Again,  adhe- 
sion holds  the  chalk  to  the  blackboard,  while  cohesion  holds 
together  the  particles  of  the  crayon. 

112.  Properties  of  solids  depending  on  cohesion.    Many  of  the 
physical  properties  in  which  solid  substances  differ  from  one 
another  depend  on  differences  in  the  cohesive  forces  existing 
between  their  molecules.   Thus,  we  are  accustomed  to  classify 
solids  with  relation  to  their  hardness,  brittleness,  ductility, 
malleability,  tenacity,  elasticity,  etc.    The  last  two  of  these 
terms  have  been  sufficiently  explained  in  the  preceding  para- 
graphs; but  since   confusion  sometimes   arises   from  failure 
to  understand  the  first  four,   the  tests  for  these  properties 
are  here  given. 

We  test  the  relative  hardness  of  two  bodies  by  seeing 
which  will  scratch  the  other.  Thus,  the  diamond  is  the 
hardest  of  all  substances,  since  it  scratches  all  others  and 
is  scratched  by  none  of  them. 


MOLECULAR  FORCES  IN  LIQUIDS  93 

We  test  the  relative  brittleness  of  two  substances  by 
seeing  which  will  break  the  more  easily  under  a  blow  from  a 
hammer.  Thus,  glass  and  ice  are  very  brittle  substances ; 
lead  and  copper  are  not. 

We  test  the  relative  ductility  of  two  bodies  by  seeing 
which  can  be  drawn  into  the  thinner  wire.  Platinum  is  the 
most  ductile  of  all  substances.  It  has  been  drawn  into 
wires  only  .00003  inch  in  diameter.  Glass  is  also  very 
ductile  when  sufficiently  hot,  as  may  be  readily  shown  by 
heating  it  to  softness  in  a  Bunsen  flame,  when  it  may  be 
drawn  into  threads  which  are  so  fine  as  to  be  almost  invisible. 

We  test  the  relative  malleability  of  two  substances  by 
seeing  which  can  be  hammered  into  the  thinner  sheet.  Gold, 
the  most  malleable  of  all  substances,  has  been  hammered 
into  sheets  3  0  0*0  o  o  mcn  ni  thickness. 

QUESTIONS  AND  PROBLEMS 

1.  Tell  how  you  may,  by  use  of  Hooke's  law  and  a  20-lb.  weight,  make 
the  scale  for  a  32-lb.  spring  balance. 

2.  A  broken  piece  of  wrought  iron  or  steel  may  be  welded  by  heating 
the  broken  ends  white  hot  and  pounding  them  together.    Gold  foil  is 
welded  cold  in  the  process  of  filling  a  tooth.    Explain  welding. 

3.  A  piece  of  broken  wood  may  be  mended  with  glue.    What  does 
the  glue  do? 

4.  Why  are  springs  made  of  steel  rather  than  of  copper? 

5.  If  a  given  weight  is  required  to  break  a  given  wire,  how  much 
force  is  required  to  break  two  such  wires  hanging  side  by  side  ?  to  break 
one  wire  of  twice  the  diameter  ? 

MOLECULAR  FORCES  IN  LIQUIDS.    CAPILLARY  PHENOMENA 

113.  Proof  of  the  existence  of  molecular  forces  in  liquids. 
The  facility  with  which  liquids  change  their  shape  might  lead 
us  to  suspect  that  the  molecules  of  such  substances  exert 
almost  no  force  upon  one  another,  but  a  simple  experiment 
will  show  that  this  is  far  from  true. 


94 


MOLECULAR  FORCES 


FIG.  93.    Illustrating 
cohesion  of  water 


By  means  of  sealing  wax  and  string  let  a  glass  plate  be  suspended 
horizontally  from  one  arm  of  a  balance,  as  in  Fig.  93.  After  equilibrium 
is  obtained,  let  a  surface  of  water  be  placed 
just  beneath  the  plate  and  the  beam  pushed 
down  until  contact  is  made.  It  will  be  found 
necessary  to  add  a  considerable  weight  to  the 
opposite  pan  in  order  to  pull  the  plate  away 
from  the  water.  Since  a  layer  of  water  will  be 
found  to  cling  to  the  glass,  it  is  evident  that 
the  added  force  applied  to  the  pan  has  been 
expended  in  pulling  water  molecules  away 
from  water  molecules,  not  in  pulling  glass 
away  from  water.  Similar  experiments  may 
be  performed  with  all  liquids.  In  the  case  of  % 

mercury  the  glass  will  not  be  found  to  be  wet,  showing  that  the  co- 
hesion of  mercury  is  greater  than  the  adhesion  of  glass  and  mercury. 

114.  Shape  assumed  by  a  free  liquid.  Since,  then,  every 
molecule  of  a  liquid  is  pulling  on  every  other  molecule,  any 
body  of  liquid  which  is  free  to  take  its  natural  shape,  that  is, 
which  is  acted  on  only  by  its  own  cohesive  forces,  must  draw 
itself  together  until  it  has  the  smallest  possible  surface  com- 
patible with  its  volume ;  for,  since  every  molecule  in  the  surface 
is  drawn  toward  the  interior  by  the  attraction  of  the  molecules 
within,  it  is  clear  that  molecules  must  continually  move  toward 
the  center  of  the  mass  until  the  whole  has  reached  the  most 
compact  form  possible.  Now  the  geometrical  figure  which  has 
the  smallest  area  for  a  given  volume  is  a  sphere.  We  conclude, 
therefore,  that  if  we  could  relieve  a  body  of  liquid  from  the 
action  of  gravity  and  other  outside  forces,  it  would  at  once 
take  the  form  of  a  perfect  sphere.  This  conclusion  may  be 
easily  verified  by  the  following  experiment: 

Let  alcohol  be  added  to  water  until  a  solution  is  obtained  in  which 
a  drop  of  common  lubricating  oil  will  float  at  any  depth.  Then  with  a 
pipette  insert  a  large  globule  of  oil  beneath  the  surface.  The  oil  will  be 
seen  to  float  as  a  perfect  sphere  within  the  body  of  the  liquid  (Fig.  94). 
(Unless  the  drop  is  viewed  from  above,  the  vessel  should  have  flat  rather 


MOLECULAR  FORCES  IN  LIQUIDS 


95 


FIG.  94.  Spherical 
globule  of  oil,  freed 
from  action  of  gravity 


than  cylindrical  sides,  otherwise  the  curved  surface  of  the  water  will 
act  like  a  lens  and  make  the  drop  appear  flattened.) 

The  reason  that  liquids  are  not  more  commonly  observed 
to  take  the  spherical  form  is  that  ordinarily  the  force  of  gravity 

is  so  large  as  to  be  more  influential  in  deter-       _= 

mining  their  shape  than  are  the  cohesive 
forces.  As  verification  of  this  statement  we 
have  only  to  observe  that  as  a  body  of 
liquid  becomes  smaller  and  smaller — that 
is,  as  the  gravitational  forces  upon  it  be- 
come less  and  less  —  it  does  indeed  tend 
more  and  more  to  take  the  spherical  form.  Thus,  very  small 
globules  of  mercury  on  a  table  will  be  found  to  be  almost 
perfect  spheres,  and  raindrops  or  minute  floating  particles  of 
all  liquids  are  quite  accurately  spherical. 

115.  Contractility  of  liquid  films;  surf  ace  tension.  The  tend- 
ency of  liquids  to  assume  the  smallest  possible  surface  fur- 
nishes a  simple  explanation  of  the  contractility  of  liquid  films. 

Let  a  soap  bubble  2  or  3  inches  in  diameter  be  blown  on  the  bowl 
of  a  pipe  and  then  allowed  to  stand.  It  will  at  once  begin  to  shrink 
in  size  and  in  a  few  minutes  will  disappear  within  the  bowl  of  the  pipe. 


FIG. 95  'FiG. 96  FIG.  97 

Illustrating  the  contractility  of  soap  films 

The  liquid  of  the  bubble  is  simply  obeying  the  tendency  to  reduce  its 
surface  to  a  minimum,  a  tendency  which  is  due  only  to  the  mutual  at- 
tractions which  its  molecules  exert  upon  one  another.  A  candle  flame 


96 


MOLECULAE  FORCES 


held  opposite  the  opening  in  the  stem  of  the  pipe  will  be  deflected  by 
the  current  of  air  which  the  contracting  bubble  is  forcing  out  through 
the  stem. 

Again,  let  a  loop  of  fine  thread  be  tied  to  a  wire  ring,  as  in  Fig.  95. 
Let  the  ring  be  dipped  into  a  soap  solution  so  as  to  form  a  film  across 
it,  and  then  let  a  hot  wire  be  thrust  through  the  film  inside  the  loop. 
The  tendency  of  the  film  outside  the  loop  to  contract  will  instantly  snap 
out  the  thread  into  a  perfect  circle  (Fig.  96).  The  reason  that  the  thread 
takes  the  circular  form  is  that,  since  the  film  outside  the  loop  is  striving 
to  assume  the  smallest  possible  surface,  the  area  inside  the  loop  must 
of  course  become  as  large  as  possible.  The  circle  is  the  figure  which 
has  the  largest  possible  area  for  a  given  perimeter. 

Let  a  soap  film  be  formed  across  the  mouth  of  a  clean  2-inch  funnel, 
as  in  Fig.  97.  The  tendency  of  the  film  to  contract  will  be  sufficient 
to  lift  its  weight  against  the  force  of  gravity. 

The  tendency  of  a  liquid  to  reduce  its  exposed  surface  to  a 
minimum,  that  is,  the  tendency  of  any  liquid  surface  to  act  like 


Fig.  98.    Some  of  the  stages  through  which  a  slowly  forming  drop  passes 

a  stretched  elastic  membrane,  is  called  surface  tension.  The  elas- 
tic nature  of  a  film  is  illustrated  in  Fig.  98,  which  is  from  a 
motion-picture  record  of  some  of  the  stages  through  which 
a  slowly  forming  drop  passes. 

116.  Ascension  and  depression  of  liquids  in  capillary  tubes. 
It  was  shown  in  Chapter  II  that,  in  general,  a  liquid  stands 
at  the  same  level  in  any  number  of  communicating  vessels. 
The  following  experiments  will  show  that  this  rule  ceases  to 
hold  in  the  case  of  tubes  of  small  diameter. 


MOLECULAR  FORCES  IN  LIQUIDS 


9T 


Let  a  series  of  capillary  tubes  of  diameter  varying  from  2  mm.  to 
.1  inm.  be  arranged  as  in  Fig.  99. 

When  water  or  ink  is  poured  into  the  vessel  it  will  be  found  to  rise 
higher  in  the  tubes  than  in  the  vessel,  and  it  will  be  seen  that  the 
smaller  the  tube  the  greater  the  height  to  which  it 
rises.    If  the  water  is  replaced  by  mercury,  however, 
the  effects  will  be   found  to  be  just  inverted.    The 
mercury  is  depressed  in  all  the  tubes,  the  depression 
being  greater  in  proportion  as  the  tube  is  smaller 
(Fig.  100,  (1)).     This  depression  is  most  easily  ob- 
served with  a  U-tube  like  that  shown  in  Fig.  100,  (2). 

Experiments  of  this  sort  have  established 
the  following  laws: 

1.  Liquids  rise  in  capillary  tubes  when  they    FlG-  "•    Rise  of 

7  7        />,,•,  7  T  -i     liquids  in  capillary 

are  capable  oj  wetting  them,  but  are  depressed  tubes 

in  tubes  which  they  do  not  wet. 

2.  The  elevation  in  the  one  case  and  the  depression  in  the 
oilier  are  inversely  proportional  to  the  diameters  of  the  tubes. 

It  will  be  noticed,  too,  that  when  a  liquid  rises,  its  surface 
within  the  tube  is  concave  upward,  and  when  it  is  depressed 
its  surface  is  convex  upward. 

117.  Cause  of  curvature  of 
a  liquid  surface  in  a  capillary 
tube.  All  of  the  effects  pre- 
sented in  the  last  paragraph 
can  be  explained  by  a  consider- 
ation of  cohesive  and  adhesive 
forces.  However,  throughout 
the  explanation  we  must  keep 
in  mind  two  familiar  facts :  first,  that  the  surface  of  a  body 
of  water  at  rest,  for  example  a  pond,  is  at  right  angles  to  the 
resultant  force,  that  is,  gravity,  which  acts  upon  it;  and,  second, 
that  the  force  of  gravity  acting  on  a  minute  amount  of  liquid  is 
negligible  in  comparison  with  its  own  cohesive  force  (see  §  114). 


FIG.  100.    Depression  of  mercury  in 
capillary  tubes 


98 


MOLECULAR  FORCES 


Consider,  then,  a  very  small  body  of  liquid  close  to  the 
point  o  (Fig.  101),  where  water  is  in  contact  with  the  glass 
wall  of  the  tube.     Let  the  quantity  of  liquid  considered  be 
so  minute  that  the 
force  of  gravity  act- 
ing    upon    it    may 
be  disregarded.  The 
force  of  adhesion  si 
the   wall   will   pull 
the  liquid  particles 


FIG.  101  FIG.  102 

Condition  for  elevation  of  a  liquid  near  a  wall 


at  o  in  the  direction 
oE.  The  force  of 
cohesion  of  the  liquid 
will  pull  these  same  particles  in  the  direction  oF.  The  resul- 
tant of  these  two  pulls  on  the  liquid  at  o  will  then  be  repre- 
sented by  oR  (Fig.  101),  in  accordance  with  the  parallelogram 
law  of  Chapter  V.  If,  then,  the  resultant  oR  of  the  adhesive 
force  oE  and  the  cohesive  force  oF  lies  to  the  left  of  the 
vertical  om  (Fig.  102),  since  the  surface  of  a  liquid  always 
assumes  a  position  at  right  angles  to 
the  resultant  force,  the  liquid  must  rise 
up  against  the  wall  as  water  does 
against  glass  (Fig.  102). 

If  the  cohesive  force  0^(Fig.  103)  is 
strong  in  comparison  with  the  adhesive 
force  oE,  the  resultant  oR  will  fall  to 
the  right  of  the  vertical,  in  which  case 
the  liquid  must  be  depressed  about  o. 

Whether,    then,    a    liquid    will    rise 

against  a  solid  wall  or  be  depressed  by  it  will  depend  only 
on  the  relative  strengths  of  the  adhesion  of  the  wall  for  the 
liquid  and  the  cohesion  of  the  liquid  for  itself.  Since  mercury 
does  not  wet  glass,  we  know  that  cohesion  is  here  relatively 
strong,  and  we  should  expect,  therefore,  that  the  mercury 


F 

FIG.  103.    Condition  for 

the  depression  of  a  liquid 

near  a  wall 


MOLECULAR  FORCES  IN  LIQUIDS 


99 


would  be  depressed,  as  indeed  we  find  it  to  be.  The  fact 
that  water  will  wet  glass  indicates  that  in  this  case  adhesion 
is  relatively  strong,  and  hence  we  should  expect  water  to  rise 
against  the  walls  of  the  containing  vessel,  as  in  fact  it  does. 

It  is  clear  that  a  liquid  which  is  depressed  near  the  edge 
of  a  vertical  solid  wall  must  assume  within  a  tube  a  surface 
which  is  convex  upward,  while  a  liquid  which  rises  against  a 
wall  must  within  such  a  tube  be  concave  upward. 

118.  Explanation  of  ascension  and  depression  in  capillary 
tubes.  As  soon  as  the  curvatures  just  mentioned  are  pro- 
duced, the  concave  surface  aob  (Fig.  104)  tends,  by  virtue  of 


FIG. 104  FIG.  105 

A  concave  meniscus  causes  a  rise 
in  a  capillary  tube 


FIG.  106 


FIG. 107 


A  convex  meniscus  causes 
a  fall 


surface  tension,  to  straighten  out  into  the  flat  surface  ao'b. 
But  it  no  sooner  thus  begins  to  straighten  out  than  adhesion 
again  elevates  it  at  the  edges.  It  will  be  seen,  therefore, 
that  the  liquid  must  continue  to  rise  in  the  tube  until  the 
weight  of  the  volume  of  liquid  lifted,  namely  amnb  (Fig.  105), 
balances  the  tendency  of  the  surface  aob  to  flatten  out.  That 
the  liquid  will  rise  higher  in  a  small  tube  than  in  a  large 
one  is  to  be  expected,  since  the  weight  of  the  column  of 
liquid  to  be  supported  in  the  small  tube  is  less. 

The  convex  mercury  surface  aob  (Fig.  106)  falls  until  the 
upward  pressure  at  0,  due  to  the  depth  h  of  mercury  (Fig.  107), 
balances  the  tendency  of  the  surface  aob  to  flatten. 


100 


MOLECULAK  FOBCES 


119.  Capillary  phenomena  in  everyday  life.    Capillary  phe- 
nomena play  a  very  important  part  in  the  processes  of  nature 
and  of  everyday  life.    Thus  the  rise  of  oil  in  wicks  of  lamps, 
the  complete  wetting  of  a  towel  when  one  end  of  it  is  allowed 
to  stand  in  a  basin  of  water,  the  rapid  absorption  of  liquid  by 
a  lump  of  sugar  when  one  corner  of  it  only  is  immersed,  the 
taking  up  of  ink  by  blotting  paper,  are  all  illustrations  of  pre- 
cisely the  same  phenomena  which  we  observe  in  the  capillary 
tubes  of  Fig.  99. 

120.  Floating  of  Small  Objects  On  water.    Let  a  needle  be  laid 
very  carefully  on  the  surface  of  a  dish  of  water.    In  spite  of  the  fact 
that  it  is  nearly  eight  times  as  dense  as  water  it  will 

be  found  to  float.  If  the  needle  has  been  previously 
magnetized,  it  may  be  made  to  move  about  in  any 
direction  over  the  surface  in  obedience  to  the  pull  of 
a  magnet  held,  for  example,  underneath  the  table.  FIG.  108.  Cross 

section      of      a 
To  discover  the   cause    ot    this   apparently     floating  needle 

impossible   phenomenon,   examine   closely   the 

surface  of  the  water  in  the  immediate  neighborhood  of  the 

needle.    It  will  be  found  to  be  depressed  in  the  manner  shown 

in  Fig.  108.    This  furnishes  at  once  the  explanation.    So  long 

as  the  needle  is  so  small  that  its  own  weight  is  no  greater  than 

the  upward  force  exerted  upon  it  by 

the  tendency  of  the   depressed   (and 

therefore   concave)  liquid   surface   to 

straighten  out  into  a  flat  surface,  the 

needle  cannot  sink  in  the  liquid,  no 

matter  how  great  its  density.    If  the 

water  had  wet  the  needle,  that  is,  if  it  had  risen  about  the 

needle  instead  of  being  depressed,  the  tendency  of  the  liquid 

surface  to  flatten  out  would  have  pulled  it  down  into  the 

liquid  instead  of  forcing  it  upward.    Any  body  about  which 

a  liquid  is  depressed  will  therefore  float  on  the  surface  of 

the  liquid  if  its  mass  is  not  too  great.     Even  if  the  liquid 


FIG.  109.    Insect  walking 
on  the  surface  of  water 


MOLECULAK  FORCES  IN  LIQUIDS  101 

tends  to  rise  about  a  body  when  it  is  perfectly  clean,  an  im- 
perceptible film  of  oil  upon  the  body  will  cause  it  to  depress 
the  liquid,  and  hence  to  float. 

The  above  experiment  explains  the  familiar  phenomenon  of 
insects  walking  and  running  on  the  surface  of  water  (Fig.  109) 
in  apparent  contradiction  to  the  law  of  Archimedes,  in  ac- 
cordance with  which  they  should  sink  until  they  displace  their 
own  weight  of  the  liquid. 

QUESTIONS  AND  PROBLEMS 

1.  Explain  how  capillary  attraction  comes  usefully  into  play  in  the 
steel  pen,  camel's-hair  brushes,  lamp  wicks,  and  sponges. 

2.  Candle  grease  may  be  removed  from  clothing  by  covering  it  with 
blotting  paper  and  then  passing  a  hot  flatiron  over  the  paper.    Explain. 

3.  Why  will  a  piece  of  sharp-cornered  glass  become  rounded  when 
heated  to  redness  in  a  Bunsen  flame  ? 

4.  The  leads  for  pencils  are  made  by  subjecting  powdered  graphite 
to  enormous  pressures  produced  by  hydraulic  machines.    Explain  how 
the  pressure  changes  the  powder  to  a  coherent  mass. 

5.  Float  two  matches  an  inch  apart.    Touch  the  water  between  them 
with  a  hot  wire.    The  matches  will  spring  apart.    What  does  this  show 
about  the  effect  of  temperature  on  surface  tension  ? 

6.  Repeat  the  experiment,  touching  the  water  with  a  wire  moistened 
with  alcohol.    What  do  you  infer  as  to  the  relative  surface  tensions  of 
alcohol  and  water? 

7.  Fasten  a  bit  of  gum  camphor  to  one  end  of  half  a  toothpick  and 
lay  it  upon  the  surface  of  a  large  vessel  of  clean  still  water.    Explain  the 
motion. 

8.  Shot  are  made  by  pouring  molten  lead  through  a  sieve  on  top 
of  a  tall  tower  and  catching  it  in  water  at  the  bottom.    Why  are  the 
shot  spherical? 

9.  Explain  how  capillary  attraction    makes   an  irrigation  system 
successful. 

10.  In  building  a  macadam  road  coarse  stones  are  placed  at  the 
bottom,  on  top  of  them  smaller  stones,  and  finally  little  granules  tightly 
rolled  together  by  means  of  a  steam  roller.    Explain  how  this  arrange- 
ment of  material  keeps  the  road  dry. 

11.  What  force  is  mainly  responsible  for  the  return  of  the  water 
that  has  gravitated  into  the  soil?    Would  the  looseness  of  the  soil  make 
any  difference  (dry  farming)  ? 


102 


MOLECULAR  FORCES 


ABSORPTION  OF  GASES  BY  SOLIDS  AND  LIQUIDS 

121 .  Absorption  Of  gases  by  solids.  Let  a  large  test  tube  be  filled 
with  ammonia  gas  by  heating  aqua  ammonia  and  causing  the  evolved 
gas  to  displace  mercury  in  the  tube,  as  in  Fig.  110.  Let  a  piece  of 
charcoal  an  inch  long  and  nearly 
as  wide  as  the  tube  be  heated 
to  redness  and  then  plunged  be- 
neath the  mercury.  When  it  is 
cool,  let  it  be  slipped  underneath 
the  mouth  of  the  test  tube  and 
allowed  to  rise  into  the  gas.  The 
mercury  will  be  seen  to  rise  in 
the  tube,  as  in  Fig.  111.  Why?  FIG.  110.  Filling  tube  with  ammonia 

This  property  of  absorbing  gases  is  possessed  to  a  notable 
degree  by  porous  substances,  especially  coconut  and  peach-pit 
charcoal.  It  is  not  improbable  that  all  solids  hold,  closely 
adhering  to  their  surfaces,  thin  layers  of  the  gases  with  which 
they  are  in  contact,  and  that  the  prominence 
of  the  phenomena  of  absorption  in  porous 
substances  is  due  to  the  great  extent  of  sur- 
face possessed  by  such  substances. 

That  the  same  substance  exerts  widely 
different  attractions  upon  the  molecules  of 
different  gases  is  shown  by  the  fact  that  char- 
coal will  absorb  90  times  its  own  volume  of 
ammonia  gas,  35  times  its  volume  of  carbon 
dioxide,  and  only  1.7  times  its  volume  of 
hydrogen.  The  usefulness  of  charcoal  as  a 
deodorizer  is  due  to  its  enormous  ability  to  absorb  certain 
kinds  of  gases.  This  property  made  it  available  for  use  in  gas 
masks  (see  opposite  p.  103)  during  the  World  War.  If  a 
little  spongy  platinum  is  suspended  in  a  vessel  above  wood 
alcohol,  it  will  glow  brightly  because  of  the  absorption  into 
the  platinum  of  both  vapor  of  alcohol  and  oxygen.  The  rapid 


FIG.  111.    Absorp- 
tion   of    ammonia 
gas  by  charcoal 


JAMES  CLERK-MAXWELL 

(1831-1879) 

One  of  the  greatest  of  mathemati- 
cal physicists  ;  born  in  Edinburgh, 
Scotland ;  professor  of  natural 
philosophy  at  Marischal  College, 
Aberdeen,  in  1856,  of  physics  and 
astronomy  in  Kings  College,  Lon- 
don, in  I860,  and  of  experimental 
physics  in  Cambi'idge  University 
from  1871  to  1879  ;  one  of  the  most 
prominent  figures  in  the  develop- 
ment of  the  kinetic  theory  of 
gases  and  the  mechanical  theory 
of  heat ;  author  of  the  electro- 
magnetic theory  of  light  — a  the- 
ory which  has  become  the  basis  of 
nearly  all  modern  theoretical  work 
in  electricity  and  optics  (see  p.  426) 


HEINRICH  RUDOLPH  HERTZ 

(1857-1894) 

One  of  the  most  brilliant  of  Ger- 
man physicists,  who,  in  spite  of  his 
early  death  at  the  age  of  thirty- 
seven,  made  notable  contributions 
to  theoretical  physics,  and  left  be- 
hind the  epoch-making  experimen- 
tal discovery  of  the  electromagnetic 
waves  predicted  by  Maxwell.  Wire- 
less telegraphy  is  but  an  applica- 
tion of  this  discovery  of  so-called 
"  Hertzian  "  waves  (see  p.  422).  The 
capital  discovery  that  ultra-violet 
light  discharges  negatively  electri- 
fied bodies  is  also  due  to  Hertz 


A  GAS  MASK 


©  U.  S.  Official 


A  great  variety  of  poisonous  gases  having  a  density  greater  than  air  were  set  free 
and  carried  by  the  wind  against  the  Allied  armies  in  the  World  War.  and  others 
were  fired  in  explosive  shells.  Until  gas  masks  were  devised  these  gases,  settling 
into  the  trenches,  wrought  frightful  havoc  among  the  troops.  The  absorptive  power 
of  charcoal,  especially  when  impregnated  with  certain  chemicals,  proved  an  effec- 
tive barrier  against  the  deadly  fumes,  since  all  of  the  air  entering  the  lungs  of 
the  soldiers  had  to  be  inhaled  through  the  charcoal  within  a  canister  carried  in 
the  bag  designed  to  hold  the  gas  mask.  The  illustration  shows  an  American  gas 
mask  adjusted  to  the  head  of  an  American  soldier 


MOLECULAR   FORCES   IX  LIQUIDS  103 

rise  in  temperature  is  due  to  the  increased  rate  of  oxidation 
of  the  alcohol  brought  about  by  this  more  intimate  mixture. 
This  property  of  platinum  is  utilized  in  the  platinum-alcohol 
cigar  lighter  (Fig.  112). 

122.  Absorption  of  gases  in  liquids. 

Let  a  beaker  containing  cold  water  be  slowly 

heated.    Small  bubbles  of  air  will  be  seen  to  Sponau 

collect  in  great  numbers  upon  the  walls  and  Platinum^ 

to    rise  through   the    liquid   to    the    surface.  Platinun 

That  they  are  indeed  bubbles  of  air  and  not  Wick 

of  steam  is  proved,  first,  by  the  fact  that  they  WoodAlcohqi 

appear  when   the  temperature   is   far  below  inCotton 
boiling,  and,  second,  by  the  fact  that  they  do 

not  condense  as  they  rise  into  the  higher  and 

FIG.  112.  The  platinum- 
cooler  layers  of  the  water.  alcohol  dgar  Hghter 

The   experiment  shows  two  things : 

first,  that  water  ordinarily  contains  considerable  quantities  of 
air  dissolved  in  it ;  and,  second,  that  the  amount  of  air  which 
water  can  hold  decreases  as  the  temperature  rises.  The  first 
point  is  also  proved  by  the  existence  of  fish  life ;  for  fishes 
obtain  the  oxygen  which  they  need  to  support  life  from  air 
which  is  dissolved  in  the  water. 

The  amount  of  gas  which  will  be  absorbed  by  water  varies 
greatly  with  the  nature  of  the  gas.  At  0°  C.  and  a  pressure  of 
76  centimeters  1  cubic  centimeter  of  water  will  absorb  1050 
cubic  centimeters  of  ammonia,  1.8  cubic  centimeters  of  carbon 
dioxide,  and  only  .04  cubic  centimeter  of  oxygen.  Commercial 
aqua  ammonia  is  simply  ammonia  gas  dissolved  in  water. 

The  following  experiment  illustrates  the  absorption  of 
ammonia  by  water : 

Let  the  flask  F  (Fig.  113)  and  tube  b  be  filled  with  ammonia  by  passing 
a  current  of  the  gas  in  at  a  and  out  through  b.  Then  let  a  be  corked 
up  and  b  thrust  into  G,  a  flask  nearly  filled  with  water  which  has  been 
colored  slightly  red  by  the  addition  of  litmus  and  a  drop  or  two  of  acid. 
As  the  ammonia  is  absorbed  the  water  will  slowly  rise  in  b,  and  as  soon 


104 


MOLECULAR  FORCES 


FIG.  113.   Absorp- 
tion   of    ammonia 
by  water 


as  it  reaches  F  it  will  rush  up  very  rapidly  until  the  upper  flask  is 
nearly  full.  At  the  same  time  the  color  will  change  from  red  to  blue 
because  of  the  action  of  the  ammonia  upon  the  litmus. 

Experiment  shows  that  in  every  case  of  ab- 
sorption of  a  gas  by  a  liquid  or  a  solid  the 
quantity  of  gas  absorbed  decreases  with  an  in- 
crease in  temperature,  —  a  result  which  was 
to  have  been  expected  from  the  kinetic 
theory,  since  increasing  the  molecular  veloc- 
ity must  of  course  increase  the  difficulty 
which  the  adhesive  forces  have  in  retaining 
the  gaseous  molecules. 

123.  Effect  of  pressure  upon  absorption. 
Soda  water  is  ordinary  water  which  has  been 
made  to  absorb  large  quantities  of  carbon 
dioxide  gas.  This  impregnation  is  accom- 
plished by  bringing  the  water  into  contact 
with  the  gas  under  high  pressure.  As  soon  as  the  pressure  is 
relieved,  the  gas  passes  rapidly  out  of  solution.  This  is  the 
cause  of  the  characteristic  effervescence  of  soda  water.  These 
facts  show  clearly  that  the  amount  of  carbon  dioxide  which  can 
be  absorbed  by  water  is  greater  for  high  pressures  than  for  low. 
As  a  matter  of  fact,  careful  experiments  have  shown  that  the 
amount  of  any  gas  absorbed  is  directly  proportional  to  the  pres- 
sure, so  that  if  carbon  dioxide  under  a  pressure  of  10  atmos- 
pheres is  brought  into  contact  with  water,  ten  times  as  much 
of  the  gas  is  absorbed  as  if  it  had  been  under  a  pressure  of 
1  atmosphere.  This  is  known  as  Henry's  law. 

QUESTIONS  AND  PROBLEMS 

1.  Why  do  fishes  in  an  aquarium  die  if  the  wrater  is  not  frequently 
renewed  ? 

2.  Explain  the  apparent  generation  of  ammonia  gas  when  aqua 
ammonia  is  heated. 

3.  Why,  in  the  experiment  illustrated  in  Fig.  113,  was  the  flow  so 
much  more  rapid  after  the  water  began  to  run  over  into  -F? 


CHAPTER  VII 

WORK  AND  MECHANICAL  ENERGY* 
DEFINITION  AND  MEASUREMENT  OF 


124.  Definition  of  work.  Whenever  a  force  moves  a  body 
on  which  it  acts,  it  is  said  to  do  work  upon  that  body,  and 
the  amount  of  the  work  accomplished  is  measured  by  the 
product  of  the  force  acting  and  the  distance  through  which 
it  moves  the  body.  Thus,  if  i  gram  of  mass  is  lifted  1  centi- 
meter in  a  vertical  direction,  1  gram  of  force  has  acted,  and 
the  distance  through  which  it  has  moved  the  body  is  1  centi- 
meter. We  say,  therefore,  that  the  lifting  force  has  accom- 
plished 1  gram  centimeter  of  work.  If  the  gram  of  force  had 
lifted  the  body  upon  which  it  acted  through  2  centimeters, 
the  work  done  would  have  been  2  gram  centimeters.  If  a 
force  of  3  grams  had  acted  and  the  body  had  been  lifted 
through  3  centimeters,  the  work  done  would  have  been  9  gram 
centimeters,  etc.  Or,  in  general,  if  W  represent  the  work 
accomplished,  F  the  value  of  the  acting  force,  and  s  the  dis- 
tance through  which  its  point  of  application  moves,  then  the 
definition  of  work  is  given  by  the  equation 

W=Fxs.  (1) 

In  the  scientific  sense  no  work  is  ever  done  unless  the 
force  succeeds  in  producing  motion  in  the  body  on  which  it 

*  It  is  recommended  that  this  chapter  be  preceded  by  an  experiment  in 
which  the  student  discovers  for  himself  the  law  of  the  lever,  that  is,  the 
principle  of  moments  (see,  for  example,  Experiment  16,  authors'  Manual), 
and  that  it  be  accompanied  by  a  study  of  the  principle  of  work  as  exempli- 
fied in  at  least  one  of  the  other  simple  machines  (see,  for  example,  Experi- 
ment 17,  authors'  Manual). 

105 


106  WORK  AND  MECHANICAL  ENERGY 

acts.  A  pillar  supporting  a  building  does  110  work ;  a  man 
tugging  at  a  stone,  but  failing  to  move  it,  does  no  work. 
In  the  popular  sense  we  sometimes  say  that  we  are  doing  work 
when  we  are  simply  holding  a  weight  or  doing  anything  else 
which  results  in  fatigue;  but  in  physics  the  word  "work"  is 
used  to  describe  not  the  effort  put  forth  but  the  effect  ac- 

A  tA/ 

complished,  as  represented  in  equation  (1). 

125.  Units  of  work.  There  are  two  common  units  of  work 
in  the  metric  system,  the  gram  centimeter  and  the  kilogram 
meter.  As  the  names  imply,  the  gram  centimeter  is  the  work 
done  by  a  force  of  1  gram  when  it  moves  the  point  on  which 
it  acts  1  centimeter.  The  kilogram  meter  is  the  work  done 
by  a  kilogram  of  force  -./hen  it  moves  the  point  on  which  it 
acts  1  meter.  The  gram  meter  also  is  sometimes  used. 

Corresponding  to  the  English  unit  o^  force,  the  pound,  is 
the  unit  of  work,  the  foot  pound.  It  is  the  work  done  by  a 
"  pound  of  force  "  when  it  moves  the  point  on  which  it  acts 
1  foot.  Thus,  it  takes  a  foot  pound  of  work  to  lift  a  pound 
of  mass  1  foot  high. 

In  the  absolute  system  of  units  the  dyne  is  the  unit  of  force,  and  the 
dyne  centimeter,  or  erg,  is  the  corresponding  unit  of  work.  The  erg  is 
the  amount  of  work  done  by  a  force  of  1  dyne  when  it  moves  the  point 
on  which  it  acts  1  centimeter.  To  raise  1  liter  of  water  from  the  floor 
to  a  table  1  meter  high  would  require  1000  x  980  X 100  =  98,^00,000  ergs 
of  work.  It  will  be  seen,  therefore,  that  the  erg  is  an  exceedingly  small 
unit.  For  this  reason  it  is  customary  to  employ  a  unit  which  is  equal 
to  10,000,000  ergs.  It  is  called  a  joule,  in  honor  of  the  great  English 
physicist  James  Prescott  Joule  (1818-1889).  The  work  done  in  lifting 
a  liter  of  water  1  meter  is  therefore  9.8  joules. 

QUESTIONS  AND  PROBLEMS 

1.  To  drag  a  trunk  weighing  120  Ib.  required  a  force  of  40  Ib.    How 
much  work  would  be  required  to  drag  this  trunk  2  yd.  ?  to  lift  it  2  yd. 
vertically  ? 

2.  A  carpenter  pushed  5  Ib.  on  his  plane  while  taking  off  a  shaving 
4  ft.  long.    How  much  work  was  done? 


WOEK  AND  THE  PULLEY  10T 

3.  How  many  foot  pounds  of  work  does  a  150-lb.  man  do  in  climbing 
to  the  top  of  Mt.  Washington,  which  is  6300  ft.  high  ? 

4.  A  horse  pulls  a  metric  ton  of  coal  to  the  top  of  a  hill  30  m.  high. 
Express  the  work  accomplished  in  kilogram  meters  (a  metric  ton  = 
1000  kg.). 

5.  If  the  20,000  inhabitants  of  a  city  use  an  average  of  20  liters  of 
water  per  capita  per  day,  how  many  kilogram  meters  of  work  must  the 
engines  do  per  day  if  the  water  has  to  be  raised  to  a  height  of  75  m.  ? 

WORK  EXPENDED  UPON  AND  ACCOMPLISHED  BY  SYSTEMS 

OF  PULLEYS 

126.  The  single  fixed  pulley.  Let  the  force  of  the  earth's  attrac- 
tion upon  a  mass  R  be  overcome  by  pulling  upon  a  spring  balance  S, 
in  the  manner  shown  in  Fig.  114,  until  R  moves  slowly  upward.  If  R 
is  100  grams,  the  spring  balance  will  also  be  found  to  t  f 

register  a  force  of  100  grams.  /HFT 

Experiment  therefore  shows  that  in  the  use 
of  the  single  fixed  pulley  the  acting  force,  or 
effort,  E,  which  is  producing  the  motion,  is  equal 
to  the  resisting  force,  or  resistance,  JK,  which  is 
opposing  the  motion. 

Again,  since  the  length  of  the  string  is  always          \    A 
constant,  the  distance  s  through  which  the  point         E 
A,  at  which  E  is  applied,  must  move  is  always     FIG.  114.  The 
equal  to  the  distance  s'  through  which  the  weight     smsle      fixed 
R  is  lifted.    Hence,  if  we  consider  the  work  put 
into  the  system  at  A,  namely,  E  x  «,  and  the  work  accomplished 
by  the  system  at  R,  namely,  R  x  s',  we  find,  obviously,  since 
R  =  E  and  s  =  *',  that 

Exs  =  fixs';  (2) 

that  is,  in  the  case  of  the  single  fixed  pulley,  the  work  done 
by  the  acting  force  E  (the  effort)  is  equal  to  the  work  done 
against  the  resisting  force  R  (the  resistance),  or  the  work  put 
into  the  machine  at  A  is  equal  to  the  work  accomplished  by 
the  machine  at  R. 


108 


WOBK  AND  MECHANICAL  ENEKGY 


127.  The  single  movable  pulley.   Now  let  the  force  of  the  earth's 
attraction  upon  the  mass  R  be  overcome  by  a  single  movable  pulley,  as 
shown  in  Fig.  115.    Since  the  weight  of  R  (R  repre- 
senting in  this  case  the  weight  of  both  the  pulley  and 
the  suspended  mass)  is  now  supported  half  by  the  strand 
C  and  half  by  the  strand  B,  the  force  E  which  must  act 
at  A  to  hold  the  weight  in  place,  or  to  move  it  slowly 
upward  if  there  is  no  friction,  should  be  only  one  half 
of  R.    A  reading  of  the  balance  will  show  that  this  is 
indeed  the  case. 

Experiment  thus  shows  that  in  the  case  of  the 
single  movable  pulley  the  effort  E  is  just  one  half 
as  great  as  the  resistance  R. 

But  when  we  again  consider  the  work  which 
the  force  E  must  clo  to  lift  the  weight  R  a  dis- 


tance *',  we   see  that  A  must  move  upward  2 


FIG.  115.    The 

single  movable 
pulley 

inches  in  order  to  raise  R    1  inch;   for  when 

R  moves  up  1  inch,  both  of  the  strands  B  and  C  must  be 

shortened  1  inch.    As  before,  therefore,  since  R  =  2  E  and 


that  is,  in  the  case  of  the  single  movable  pulley,  as  in  the 
•case  of  the  fixed  pulley,  the  work  put  into  the  machine  by  the 
•effort  E  is  equal  to  the  work  accomplished  by  the  machine  against 

the  resistance  R. 

• 

128.  Combinations  of  pulleys.  Let  a  weight  R  be  lifted  by  means 
•of  such  a  system  of  pulleys  as  is  shown  in  Fig.  116,  either  (1)  or  (2). 
Here,  since  R  is  supported  by  6  strands  of  the  cord,  it  is  clear  that  the 
force  which  must  be  applied  at  A  in  order  to  hold  R  in  place,  or  to 
make  it  move  slowly  upward  if  there  is  no  friction,  should  be  but  i  of  R. 

The  experiment  will  show  this  to  be  the  case  if  the  effects 
of  friction,  which  are  often  very  considerable,  are  eliminated 
'by  taking  the  mean  of  the  forces  which  must  be  applied  at  E 
to  cause  it  to  move  first  slowly  upward  and  then  slowly  down- 
ward. The  law  of  any  combination  of  movable  pulleys  may 


WORK  AND  THE  PULLEY 


109 


then  be  stated  thus :    If  n  represents  the  number  of  strands 
between  which  the  weight  is  divided, 

E  =  R/n.  (3) 

But  when  we  again  consider  the  work  which  the  force  E 
must  do  in  order  to  lift  the  weight  R  through  a  distance  *', 
we  see  that,  in  order  that  the  weight 
R  may  be  moved  up  through  1  inch, 
each  of  the  strands  must  be  short- 
ened 1  inch,  and  hence  the  point  A 
must  move  through  n  inches ;  that 
is,  s'  =  s/n.  Hence,  ignoring  friction, 
in  this  case  also  we  have 


(i) 


E  X  s  =  R  x  sf ; 

that  is,  although  the  effort  E  is  only 
-  of  the  resistance  R,  the  work  put 


n 


FIG.  116.    Combinations 
of  pulleys 


into  the  machine  by  the  effort  E  is 
equal  to  the  work  accomplished  by  the 
machine  against  the  resistance  R. 

129.  Mechanical  advantage.   The 
above  experiments  show  that  it  is 

sometimes  possible  by  applying  a  small  force  E  to  overcome 
a  much  larger  resisting  force  R.  The  ratio  of  the  resistance  R 
to  the  effort  E  (ignoring  friction)  is  called  the  mechanical  advan- 
tage of  the  machine.  Thus,  the  mechanical  advantage  of  the 
single  fixed  pulley  is  1,  that  of  the  single  movable  pulley  is 
2,  that  of  the  system  of  pulleys  shown  in  Fig.  116  is  6,  etc. 

If  the  acting  force  is  applied  at  R  instead  of  at  E  the  me- 
chanical advantage  of  the  systems  of  pulleys  of  Fig.  116  is  i ; 
for  it  requires  an  application  of  6  pounds  at  R  to  lift  1  pound 
at  E.  But  it  will  be  observed  that  the  resisting  force  at  jE'now 
moves  six  times  as  fast  and  six  times  as  far  as  the  acting  force 
at  R.  We  can  thus  either  sacrifice  speed  to  gain  force,  or 


110     WOEK  AND  MECHANICAL  ENERGY 

sacrifice  force  to  gain  speed ;  but  in  every  case,  whatever  we 
gain  in  the  one  we  lose  in  the  other.  Thus  in  the  hydraulic 
elevator  shown  in  Fig.  13,  p.  18,  the  cage  moves  only  as  fast 
as  the  piston ;  but  in  that  shown  in  Fig.  14  it  moves  four  times 
as  fast.  Hence  the  force  applied  to  the  piston  in  the  latter 
case  must  be  four  times  as  great  as  in  the  former  if  the  same 
load  is  to  be  lifted.  This  means  that  the  diameter  of  the  latter 
cylinder  must  be  twice  as  great. 

QUESTIONS  AND  PROBLEMS 

1.  Although  the  mechanical  advantage  of  the  fixed  pulley  is  only  1, 
it  is  extensively  used  in  connection  with  clothes  lines,  awnings,  open 
wells,  and  flags.    Explain. 

2.  If  the  hydraulic  elevator  of  Fig.  14,  p.  18,  is  to  carry  a  total  load 
of  20,000  lb.,  what  force  must  be  applied  to  the  piston?   If  the  water 
pressure  is  70  lb.  per  square  inch,  what  must  be  the  area  of  the  piston? 

3.  Draw  a  diagram  of  a  set  of  pulleys  by  which  a  force  of  50  lb.  can 
support  a  load  of  200  lb. 

4.  Draw  a  diagram  of  a  set  of  pulleys  by  which  a  force  of  50  lb.  can 
support  250  lb.    What  would   be   the  mechanical  advantage  of   this 
arrangement  ? 

5.  Two  men,  pulling  50  lb.  each,  lifted  300  lb.  by  a  system  of  pulleys. 
Assuming  no  friction,  how  many  feet  of  rope  did  they  pull  down  in 
raising  the  weight  20  f  t.  ? 

WORK  AND  THE  LEVER 

130.  The  law  of  the  lever.    The  lever  is  a  rigid  rod  free 
to  turn  about  some  point  P  called  the  fulcrum  (Fig.  117). 

First  let  a  meter 
stick  be  balanced  as 
in  the  figure,  and 
then  let  a  mass  of, 
say,  300  g.  be  hung 

by  a  thread  from  a  ' ' 

point    15  cm.    from  FIG.  117.    The  simple  lever 

the  fulcrum.    Then 

let  a  point  be  found  on  the  other  side  of  the  fulcrum  at  which  a  weight 

of  100  g.  will  just  support  the  300  g.    This  point  will  be  found  to  be 


I L__L 


J I 1 I J 


WORK  AND  THE  LEVER  111 

45  cm.  from  the  fulcrum.  Jt  will  be  seen  at  once  that  the  product  of 
300  x  15  is  equal  to  the  product  of  100  x  45. 

Next  let  the  point  be  found  at  which  150  g.  just  balance  the  300  g. 
This  will  be  found  to  be  30  cm.  from  the  fulcrum.  Again,  the  products 
300  x  15  and  150  x  30  are  equal. 

No  matter  where  the  weights  are  placed,  or  what  weights 
are  used  on  either  side  of  the  fulcrum,  the  product  of  the 
effort  E  by  its  distance  I  A  p  B 

from  the  fulcrum  (Fig.  118) 
will  be  found  to  be  equal 
to  the  product   of  the  re- 
sistance R  by  its  distance  I'  s 
from  the  fulcrum.    Now  the     ^IG.  118.  Illustrating  the  law  of  moments, 

namely,  El=Rl' 
perpendicular    distances    I 

and  I'  from  the  fulcrum  to  the  line  of  action  of  the  forces  are 
called  the  lever  arms  of  the  forces  E  and  R,  and  the  product  of 
a  force  by  its  lever  arm  is  called  the  moment  of  that  force.  The 
above  experiments  on  the  lever  may  then  be  generalized  in 
the  following  law :  The  moment  of  the  effort  is  equal  to  the 
moment  of  the  resistance.  Algebraically  stated,  it  is 

El  =  Rl'.  (4) 

It  will  be  seen  that  the  mechanical  advantage  of  the  lever, 
namely  R/E,  is  equal  to  l/l' ;  that  is,  to  the  lever  arm  of  the 
effort  divided  by  the  lever  arm  of  the  resistance. 

131.  General  laws  of  the  lever.  If  parallel  forces  are  applied 
at  several  points  on  a  lever,  as  in  Figs.  119  and  120,  it  will  be 
found,  in  the  particular  cases  illustrated,  that  for  equilibrium 

.    200  x  30  -  100  x  20  + 100  x  40 
and   300  x  20  +  50  x  40  =  100  x  15  +  200  x  32.5  ; 

that  is,  the  sum  of  all  the  moments  which  are  tending  to  turn 
the  beam  in  one  direction  is  equal  to  the  sum  of  all  the  moments 
tending  to  turn  it  in  the  opposite  direction. 


112 


WORK  AND  MECHANICAL  ENERGY 


If,  further,  we  support  the  levers  of  Figs.  119  and  120 
by  spring  balances  attached  at  P,  we  shall  find,  after  allowing 
for  the  weight  of  the  stick,  that  the  two  forces  indicated  by 
the  balances  are  respectively  200  +  100  +  100  =  400  Q 
and  300  +  100  +  200  —  50  =  550  ;  that  is,  the  sum  of 
all  the  forces  acting  in  one  direction  on  the  lever  is  equal  to 
the  sum  of  all  the  forces  act' 
ing  in  the  opposite  direction. 


200 


FIG.  119  FIG.  120 

Condition  of  equilibrium  of  a  bar  acted  upon  by  several  forces 

These  two  laws  may  be  combined  as  follows :  If  we  think 
of  the  force  exerted  by  the  spring  balance  as  the  equilibrant 
of  all  the  other  forces  acting  on  the  lever,  then  we  find  that  the 
resultant  of  any  number  of  parallel  forces  is  their  algebraic  sum, 
and  its  point  of  application  is  the  point  about  which  the  algebraic 
sum  of  the  moments  is  zero. 

132.  The  couple.    There  is  one  case,  however,  in  which  paral- 
lel forces  can  have  no  single  force  as  fheir  resultant,  namely, 
the  case  represented  in  Fig.  121.    Such  a  pair  of  equal     F 
and  opposite  forces  acting  at  different  points  on  a  lever  is 

called  a  couple  and  can  be  neutralized  *    g 

only  by  another  couple  tending  to 

produce    rotation    in    the    opposite 

direction.    The   moment   of   such    a     *      FlG' 12L  The  couPle 

couple  is  evidently  F1  X  oa  +  F2  x  ob  —  Fl  X  ab ;  that  is,  it  is 

one  of  the  forces  times  the  total  distance  between  them.    The 

forces  applied  to  the  steering  wheel  of  an  automobile  illustrate 

the  couple. 


WORK  AND  THE  LEVEE  113 

133.  Work  expended  upon  and  accomplished  by  the  lever. 
We  have  just  seen  that  when  the  lever  is  in  equilibrium  — 
that  is,  when  it  is  at  rest  or  is  moving  uniformly  —  the  relation 
between  the  effort  E  and  the  resistance  R  is  expressed  in  the 
equation  of  moments,  namely  El  =  Rlf.    Let  us  now  suppose, 
precisely  as  in  the   case   of 

the  pulleys,  that  the  force  E 
raises  the  weight  R  through 
a  small  distance  sf.  To  ac- 
complish this,  the  point  A  to  E 

which   E   is   attached    must 

,,  ,  ,.   ,  FIG.  122.    Showing  that  the  equation 

move  through  a  distance  8  Of  moments,  1W  =  £r,  is  equivalent  to 
(Fig.  122).  From  the  simi-  Es  =  Ks' 

larity  of  the  triangles  APn 

and  BPm  it  will  be  seen  that  l/l'  is  equal  to  s/s'.  Hence 
equation  (4),  which  represents  the  law  of  the  lever,  and  which 
may  be  written  E/  R  =  I' /I,  may  also  be  written  in  the  form 

E/R  =  *'/«,  or  Es  *=  Rs1. 

Now  Es  represents  the  work  done  by  the  effort  E,  and  Rs1 
tlie  work  done  against  the  resistance  R.  Hence  the  law  of 
u.  moments,  which  has  just  been  found  by  experiment  to  be  the 
law  of  the  lever,  is  equivalent  to  the  statement  that  whenever 
work  is  accomplished  l>y  the  use  of  the  lever,  the  work  expended 
upon  the  lever  by  the  effort  E  is  equal  to  the  work  accomplished 
by  the  lever  against  the  resistance  R. 

134.  The  three  classes  of  levers.    Although  the  law  stated 
in  §  133  applies  to  all  forms  of  the  lever,  it  is  customary  to 
divide  them  into  three  classes,  as  follows : 

1.  In  levers  of  the  first  class  the  fulcrum  P  is  between  the 
acting  force  E  and  the  resisting  force  R  (Fig.  123).  The 
mechanical  advantage  of  levers  of  this  class  is  greater  or  less 
than  unity  according  as  the  lever  arm  I  of  the  effort  is  greater 
or  less  than  the  lever  arm  V  of  the  resistance. 


114 


WORK  AND  MECHANICAL  ENERGY 


2.  In  levers  of  the  second  class  the  resistance  R  is  between 
the  effort  E  and  the  fulcrum  P  (Fig.  124).  Here  the  level- 
arm  of  the  effort,  that  is,  the  distance  from  E  to  P,  is  neces- 
sarily greater  than  the  lever  arm  of  the  resistance,  that  is,  the 


I ' — S7 


(1) 


(2) 


FIG.  123.   Levers  of 
first  class 


FIG.  124.    Levers  of 
second  class 


FIG.  125.   Levers  of 
third  class 


distance  from  R  to  P.    Hence  the  mechanical  advantage  of 
levers  of  the  second  class  is  always  greater  than  1. 

3.  In  levers  of  the  third  class  the  acting  force  is  between  the 
resisting  force  and  the  fulcrum  (Fig.  125).  The  mechanical 
advantage  is  then  obviously  less  than  1,  that  is.  in  this  type 
of  lever  force  is  always  sacrificed  for  the  sake  of  gaining  speed. 

QUESTIONS  AND  PROBLEMS 

1.  In  which  of  the  three   classes  of   levers  does  the  wheelbarrow 
belong?    grocer's    scales?    pliers?    sugar    tongs?    a  claw  hammer?    a 
pump  handle  ? 

2.  Explain  the  principle  of  weighing  by  the  steelyards  (Fig.  126). 
What  must  be  the  weight  of  the  bob  P  if  at  a  distance  of  40  cm.  from 
the  fulcrum  0  it  balances  a  weight  of  10  kg.  placed  at  a  distance  of 
2  cm.  from  0  ? 

3.  If  you    knew  your    own  weight,  how  could  you   determine  the 
weight  of  a  companion  if  you  had  only  a  teeter  board  and  a  foot  rule  ? 

4.  How  would  you  arrange  a  crowbar  to  use  it  as  a  lever  of  the  first 
class  in  overturning  a  heavy  object?  as  a  lever  of  the  second'class ? 

5.  Why  do  tinners'  shears  have  long  handles  and  short  blades  and 
tailors'  shears  just  the  opposite  ? 


WORK  AND  THE  LEVER 


115 


FIG.  126.    Steelyards 


6.  By  reference  to  moments  explain  (a)  why  a  door  can  be  closed 
more  easily  by  pushing-  at  the  knob  than  at  a  point  close  to  the  hinges  ; 
(b)  why  a  heavier  load  can  be  lifted  on  a  wheelbarrow  having  long- 
handles  than  on  one  with  short  han- 
dles; (c)  why  a  long-handled  shovel 

generally  has  a   smaller  blade  than 
one  with  a  shorter  handle. 

7.  Two  boys  carry  a  load  of  60  Ib. 
on  a  pole  between  them.    If  the  load 
is  4  ft.  from  one  boy  and  6  ft.  from 
the  other,  how  many  pounds  does  each 
boy  carry?     (Consider  the  force  ex- 
erted by  one  of  the  boys  as  the  effort, 
the  load  as  the  resistance,  and  the 
second  boy  as  the  fulcrum.) 

8.  Where  must  a  load  of  100  Ib.  be  placed  on  a  stick  10  ft.  long  if 
the  man  who  holds  one  end  is  to  support  30  Ib.  while  the  man  at  the 
other  end  supports  70  Ib.  ? 

9.  One  end  of  a  piano  must  be  raised  to  remove  a  broken  caster. 
The  force  required  is  240  Ib.    Make  a  diagram  to  show  how  a  6-foot 
steel  bar  may  be  used  as  a  second-class  lever  to  raise  the  piano  with  an 
effort  of  40  Ib. 

10.  When  a  load  is  carried  on  a  stick  over  the  shoulder,  why  does 
the  pressure  on  the  shoulder  become  greater  as  the  load  is  moved  farther 
out  on  the  stick? 

11.  A  safety  valve  and  weight  are  arranged  as  in  Fig.  127.    If  ab  is 
1£  in.  and  be  101  in.,  what  effective  steam  pressure  per  square  inch  is 
required  on  the  valve  to  unseat  it,  if  the  area  of  the  valve  is  \  sq.  in. 
and  the  weight  of  the  ball  4  Ib.  ? 

12.  The  diameters  of  the  piston  and 
cylinder    of   a   hydraulic   press    are    re- 
spectively 3  in.  and  30  in.    The  piston 
rod  is  attached  2  ft.  from  the   fulcrum 
of  a  lever  12  ft.  long  (Fig.  12,  p.  17). 
What  force  must  be  applied  at  the  end 
of  the  lever  to  make  the  press  exert  a 
force  of  5000  Ib.  ? 

13.  Three  boys  sit  on  a  seesaw  as  follows :  A  (=  75  Ib.),  4  ft.  to  the 
right  of  the  fulcrum;  B  (=  100  Ib.),  7  ft.  to  the  right  of  the  fulcrum; 
C  (=  x  Ib.),  7  ft.  to  the  left  of  the  fulcrum.    Equilibrium  is  produced 
by  a  man,  12  ft.  to  the  right  of  the  fulcrum,  pushing  up  with  a  force  of 
25  Ib.    Find  C's  weight. 


FIG. 127 


116  WOEK  AND  MECHANICAL  ENERGY 

THE  PRINCIPLE  OF  WORK 

135.  Statement  of  the  principle  of  work.    The  study  of 
pulleys  led  us  to  the  conclusion  that  in  all  cases  where  such 
machines  are  used  the  work  done  by  the  effort  is  equal  to 
the  work  done  against  the  resistance,  provided  always  that 
friction  may  be  neglected  and  that  the  motions  are  uniform 
so   that  none  of  the   force  exerted  is  used  in   overcoming 
inertia.    The  study  of  levers  led  to  precisely  the  same  result. 
In  Chapter  II  the  study  of  the  hydraulic  press  showed  that 
the  same  law  applied  in  this  case  also,  for  it  was  shown  that 
the  force  on   the  small  piston  times  the  distance  through 
which  it  moved  was  equal  to  the  force  on  the  large  piston 
times  the  distance  through  which  it  moved.    Similar  experi- 
ments upon  all  sorts  of  machines  have  shown  that  the  follow- 
ing is  an  absolutely  general  law :  In  all  mechanical  devices  of 
whatever  sort,  in  all  cases  where  friction  may  ~be  neglected,  the 
work  expended  upon  the  machine  is  equal  to  the  work  accom- 
plished by  it. 

This  important  generalization,  called  "  the  principle  of 
work,"  was  first  stated  by  Newton  in  1687.  It  has  proved 
to  be  one  of  the  most  fruitful  principles  ever  put  forward 
in  the  history  of  physics.  By  its  application  it  is  easy  to 
deduce  the  relation  between  the  force  applied  and  the  force 
overcome  in  any  sort  of  machine,  provided  only  that  friction 
is  negligible  and  that  the  motions  take  place  slowly.  It  is 
only  necessary  to  produce,  or  imagine,  a  displacement  at  one 
end  of  the  machine,  and  then  to  measure  or  calculate  the 
corresponding  displacement  at  the  other  end.  The  ratio  of 
the  second  displacement  to  the  first  is  the  ratio  of  the  force 
acting  to  the  force  overcome. 

136.  The  wheel  and  axle.   Let  us  apply  the  work  principle  to 
discover  the  law  of  the  wheel  and  axle  (Fig.  128).   When  the 
large  wheel  has  made  one  revolution,  the  point  A  on  the  rope 


THE  PRINCIPLE  OF  WORK 


117 


moves  down  a  distance  equal  to  the  circumference  of  the  wheel. 
During  this  time  the  weight  R  is  lifted  a  distance  equal  to 
the  circumference  of  the  axle.  Hence  the  equa- 
tion Es  —  RsJ  becomes  E  x  2  7rRw  =  R  X  2wra, 
where  Rw  and  ra  are  the  radii  of  the  wheel  and 
axle  respectively.  This  equation  may  be  writ- 
ten in  the  form 

Rjra',  (5) 


s    as 


FIG.  128.     The 
wheel  and  axle 


that   is,   the   weight   lifted  on  the    axle 

many  times  the  force  applied  to  the  wheel  as  the 

radius  of  the  wheel  is  times  the  radius  of  the  axle. 

Otherwise  stated, 
the  mechanical  advantage  of  the  wheel 
and  axle  is  equal  to  the  radius  of 
the  ivheel  divided  Iry  the  radius  of 
the  axle. 

The  capstan  (Fig.  129)  is  a  spe- 
cial case  of  the  wheel  and  axle,  the 
length  of  the  lever  arm  taking  the 
place  of  the  radius  of  the  wheel, 
and  the  radius  of  the  barrel  corre- 
sponding to  the  radius  of  the  axle. 
137.  The  work  principle  applied  to  the  inclined  plane.  The 

work  done  against  gravity  in  lifting  a  weight  R  (Fig.  130) 

from  the  bottom  to  the  top  of  a 

plane  is  evidently  equal  to  R  times 

the  height  h  of  the  plane.    But  the 

work  done  by  the  acting  force  E 

while  the  carriage  of  weight  R  is 

being  pulled  from  the  bottom   tp 

the  top  of  the    plane  is  equal  to 

E  times  the  length  I  of  the  plane.    Hence  the  principle  of 

work  gives  m  =  Rj^  or  R/E  = 


FIG.  129.   The  capstan 


FlG  m  The  indined  pljme 


118 


WORK  AND  MECHANICAL  ENERGY 


FIG.  131.    The 

jackscrew 


that  is,  the  mechanical  advantage  of  the  inclined  plane,  or  the 
ratio  of  the  weight  lifted  to  the  force  acting  parallel  to  the  plane, 
is  the  ratio  of  the  length  of  the  plane  to  the 
height  of  the  plane.  This  is  precisely  the  con- 
clusion at  which  we  arrived  in  another  way 
in  Chapter  V,  p.  63. 

138.  The  screw.    The  screw  (Fig.  131)  is 
a  combination  of  the  inclined  plane  and   the 
lever.    Its  law  is  easily  obtained  from  the  prin- 
ciple  of  work.     When  the    force  which   acts 
on  the  end  of  the  lever  has  moved  this  point 
through  one  complete  revolution,  the  weight 

R,  which  rests  on  top  of  the  screw,  has  evidently  been  lifted 
through  a  vertical  distance  equal  to  the  distance  between  two 
adjoining  threads.  This  distance  d  is 
called  the  pitch  of  the  screw.  Hence,  if 
we  represent  by  /  the  length  of  the  lever, 
the  work  principle  gives 

that  is,  the  mechanical  advantage  of  the 
screw,  or  the  ratio  of  the-iveight  lifted  to    FIG.  132.  The  letter  press 
the  force  applied,  is  equal  to  the  ratio  of 

the  circumference  of  the  circle  moved  over  by  the  end  of  the  lever 
to  the  distance  between  the  threads  of  the  screw.  In  actual  practice 
the  friction  in  such  an  arrangement  is  always 
very  great,  so  that  the  effort  exerted  must 
always  be  considerably  greater  than  that  given 
by  equation  7.  The  common  jackscrew  just 
described  (and  used  chiefly  for  raising  build- 
ings), the  letter  press  (Fig.  132),  and  the  vise  FIG.  133.  The  vise 
(Fig.  133)  are  all  familiar  forms  of  the  screw. 

139.  A  train  of  gear  wheels.   A  form  of  machine  capable  of  very  high 
mechanical  advantage  is  the  train  of  gear  wheels  shown  in  Fig.  134. 


THE  PRINCIPLE  OF  WORK 


119 


Let  the  student  show  from  the  principle  of  work,  namely  Es  =  Rs',  that 
the  mechanical  advantage,  that  is,  -^,  of  such  a  device  is 


circum.  of  a      no.  cogs  in  d      no.  cogs  in  / 
circum.  of  e      no.  cogs  in  c      no.  cogs  in  b 


(8) 


140.  The  worm  wheel.*  Another  device  of  high  mechanical  advantage 
is  the  worm  wheel  (Fig.  135).  Show  that  if  I  is  the  length  of  the  crank 
arm  C,  n  the  number  of 
teeth  in  the  cogwheel  / 

W,  and  r  the  radius  of 
the  axle,  the  mechanical 
advantage  is  given  by 


2-Trln  _     I 
2  TIT  r 


(9) 


FIG.  134.   Train  of  gear 
wheels 


FIG.  135.  The  worm 
gear 


This  device  is  used 
most  frequently  when 
the  primary  object  is  to 
decrease  speed  rather  than  to  multiply  force.  It  will  be  seen  that  the 
crank  handle  must  make  n  turns  while  the  cogwheel  is  making  one.  The 
worm-gear  "  drive  "  is  generally  used  in  the  rear  axles  of  auto  trucks. 

141.  The  differential  pulley.  In  the  differential  pulley  (Fig.  136)  an 
endless  chain  passes  first  over  the  fixed  pulley  A,  then  down  and 
around  the  movable  pulley  C, 
then  up  again  over  the  fixed  pul- 
ley B,  which  is  rigidly  attached 
to  A,  but  differs  slightly  from  it 
in  diameter.  On  the  circumfer- 
ence of  all  the  pulleys  are  projec- 
tions which  fit  between  the  links, 
and  thus  keep  the  chains  from  slip- 
ping. When  the  chain  is  pulled 
down  at  E,  as  in  Fig.  136,  (2), 
until  the  upper  rigid  system  of 
pulleys  has  made  one  complete 
revolution,  the  chain  between  the 
upper  and  lower  pulleys  has  been 
shortened  by  the  difference  be- 
tween the  circumferences  of  the  FIG.  136.  The  differential  pulley 


120 


WORK  AND  MECHANICAL  ENERGY 


pulleys  A  and  B,  for  the  chain  has  been  pulled  up  a  distance  equal  to  the 
circumference  of  the  larger  pulley  and  let  down  a  distance  equal  to  the 
circumference  of  the  smaller  pulley.  Hence  the  load  R  has  been  lifted  by 
half  the  difference  between  the  circumferences  of  A  and  B.  The  mechan- 
ical advantage  is  therefore  equal  to  the  circumference  of  A  divided  by 
one  half  the  difference  between  the  circumferences  of  A  and  B. 


QUESTIONS  AND  PROBLEMS 

1.  A  1500-pound  safe  must  be  raised  5  ft.  The  force  which  can  be 
applied   is    250  Ib.     What  is   the    shortest  inclined  plane  which  can 
be  used  for  the  purpose? 

2.  A  300-pound  barrel  was  rolled  up  a  plank 
12  ft.  long  into  a  doorway  3  ft.  high.    What  force 
was  applied  parallel  to  the  plank  ? 

3.  A  force  of  80  kg.  on  a  wheel  whose  diameter 
is  3  m.  balances  a  weight  of  150  kg.  on  the  axle. 
Find  the  diameter  of  the  axle. 

4.  If  the  capstan  of  a  ship  is  12  in.  in  diameter 
and  the  levers  are  6  ft.  long,  what  force  must  be 
exerted  by  each  of  4  men  in  order  to  raise  an  anchor 
weighing  2000  Ib.  ? 

5.  If,    in    the    compound    lever   of    Fig.    137, 

AC  =  6  ft.,  BC=l  ft.,  DF  =  4  ft.,  FG  =  8  in.,  HJ  =  5  ft.,  and.//  =  2  ft., 
what  force  applied  at  E  will  support  a  weight  of  2000  Ib.  at  R  ? 


B 


I  H 

R  E 

FIG.  137.  The  com- 
pound lever 


FIG.  138.    Hay  scales 


FIG.  139.  Windlass  with  gears 


6.  The  hay  scales  shown  in  Fig.  138  consist  of  a  compound  lever  with 
fulcrums  at  F,  F',  F",  F'".  If  Fo  and  F'o'  are  lengths  of  6  in.,  FE  and 
F'E  5  ft.,  F"n  1  ft.,  F"m  6  ft.,  rF'"  2  in.,  and  F'"S  20  in.,  how  many 
pounds  at  W  will  be  required  to  balance  a  weight  of  a  ton  on  the  platform? 


POWER  AND  ENERGY 


121 


7.  In  the  windlass  of  Fig.  139  the  crank  handle  has  a  length  of 
2  ft.,  and  the  barrel  a  diameter  of  8  in.    There  are  20  cogs  in  the  small 
cogwheel  and  60  in  the  large  one.    What  is  the  mechanical  advantage 
of  the  arrangement? 

8.  If  in  the  crane  of  Fig.  140  the  crank  arm  has  a  length  of  J  m., 
and  the  gear  wheels  A,  B,  C,  and  D  have- respectively  12,  48, 12,  and  60 
cogs,  while  the  axle  over 

which  the  chain  runs  has 
a  radius  of  10  cm.,  what  is 
the  mechanical  advantage 
of  the  crane  ? 

9.  If    a  worm  wheel 
(Fig.  135)   has   30   teeth, 
and  the   crank  is   25  cm. 
long,  while  the  radius  of 
the  axle  is  3  cm.,  what  is 
the  mechanical  advantage 
of  the  arrangement? 

10.  A  small  jackscrew 
has  20  threads  to  the  inch. 
Using  a  lever  3^  in.  long 

will  give  what  mechanical  FIG.  140.   The  crane 

advantage?  (Use  3.1416.) 

11.  The  screw  of  a  letter  press  has  5  threads  to  the  inch,  and  the 
diameter  of  the  wheel  is  12  in.    If  there  were  no  friction,  what  pres- 
sure would  result  from  a  rotating  force  of  20  Ib.  applied  to  the  wheel  ? 

12.  Eight  jackscrews,  each  of  which  has  a  pitch  of  £  in.  and  a  lever 
arm  of  18  in.,  are  being  worked  simultaneously  to  raise  a  building  weigh- 
ing 100,000  Ib.    What  force  would  have  to  be  exerted  at  the  end  of  each 
lever  if  there  were  no  friction  ?    What  if  75  %  were  wasted  in  friction  ? 

13.  What  is  gained  by  using  a  machine  whose  mechanical  advantage 
is  -^  ?  Name  two  or  three  household  appliances  whose  mechanical  advan- 
tage is  less  than  1. 

POWER  AXD  ENERGY 

142.  Definition  of  power.  When  a  given  load  has  been 
raised  a  given  distance  a  given  amount  of  work  has  been 
done,  whether  the  time  consumed  in  doing  it  is  small  or  great. 
Time  is  therefore  not  a  factor  which  enters  into  the  deter- 
mination of  work ;  but  it  is  often  as  important  to  know  the 
rate  at  which  work  is  done  as  to  know  the  amount  of  work 


122  WORK  AND  MECHANICAL  ENERGY 

accomplished.  The  rate  of  doing  work  is  called  power,  or  activity. 
Thus,  if  P  represent  power,  W  the  work  done,  and  t  the  time 
required  to  do  it, 

P  =  -^-  (10) 

{/ 

143.  Horse  power.    James  Watt  (1736-1819),  the  inventor 
of  the  steam  engine,  considered  that  an  average  horse  could  do 
33,000  foot  pounds  of  work  per  minute,  or  550  foot  pounds  per 
second.    The  metric  equivalent  is  76.05  kilogram  meters  per 
second.    This  number  is  probabty  considerably  too  high,  but 
it  has  been  taken  ever  since,  in  English-speaking  countries, 
as  the  unit  of  power,  and  named  the  horse  power  (H.P.). 
The  power  of  steam  engines  has  usually  been  rated  in  horse 
power.    The  horse  power  of  an  ordinary  railroad  locomotive  is 
from  500  to  1000.    Stationary  engines  and  steamboat  engines 
of  the  largest  size  often  run  from  5000  to  20,000  H.P.    The 
power  of  an  average  horse  is  about  -|  H.P.,  and  that  of  an 
ordinary  man  about  ^  H.P. 

144.  The  kilowatt.    In  the  metric  system  the  erg  has  been 
taken  as  the  absolute  unit  of  work.    The  corresponding  unit  of 
power  is  an  erg  per  second.    This  is,  however,  so  small  that  it 
is  customary  to  take  as  the  practical  unit  10,000,000  ergs  per 
second  ;  that  is,  one  joule  per  second  (see  §  125,  p.  106).   This 
unit  is  called  the  watt,  in  honor  of  James  Watt.    The  power 
of  dynamos  and  electric  motors  is  almost  always  expressed  in 
kilowatts,  a  kilowatt  representing  1000  watts  ;  and  in  modern 
practice  even  steam  engines  are  being  increasingly  rated  in 
kilowatts  rather  than  in  horse  powrer.   A  horse  power  is  equiva- 
lent to  746  watts,  or  about  |  of  a  kilowatt.    A  kilowatt  is 
almost  exactly  equal  to  102  kilogram  meters  per  second. 

145.  Definition  of  energy.    The  energy  of  a  body  is  denned 
as  its  capacity  for  doing  work.    In  general,  inanimate  bodies 
possess  energy  only  because  of  work  which  has  been  done  upon 
them  at  some  previous  time.    Thus,  suppose  a  kilogram  weight 


JAMES  PRESCOTT  JOULE 
(1818-1889) 

English  physicist,  born  at  Man- 
chester ;  most  prominent  figure  in 
the  establishment  of  the  doctrine 
of  the  conservation  of  energy ; 
studied  chemistry  as  a  boy  under 
John  Dalton,  and  became  so  inter- 
ested that  his  father,  a  prosperous 
Manchester  brewer,  fitted  out  a 
laboratory  for  him  at  home  ;  con- 
ducted mostof  his  researches  either 
in  a  basement  of  his  own  house  or 
in  a  yard  adjoining  his  brewery ; 
discovered  the  law  of  heating  a 
conductor  by  an  electric  current ; 
carried  out,  in  connection  with 
Lord  Kelvin,  epoch-making  re- 
searches upon  the  thermal  prop- 
erties of  gases;  did  important  work 
in  magnetism;  first  proved  experi- 
mentally the  identity  of  various 
forms  of  energy 


JAMES  WATT  (1736-1819) 

The  Scotch  instrument  maker  at 
the  University  of  Glasgow,  who 
may  properly  be  considered  the 
inventor  of  the  steam  engine  ;  for, 
although  a  crude  and  inefficient 
type  of  steam  engine  was  known 
before  his  time,  he  left  it  in  essen- 
tially its  present  form.  The  mod- 
ern industrial  era  may  be  said  to 
begin  with  Watt 


•  =  |j  a  «  I 

If  83 II 

<D    ^    -  <M    35 

^  1 1  S  2 

O     ^     r-     C   »-H 


r   c 
^   o   « 


2  n3  <D  "S 

C      tf      M 


'  trffr? 


^    i  a  *  I  £ 

S     g  §  6^-5  5 
,5     2  g  -e  5  o 


SB  *  M  §  - 


P  111 

1 


p^ 

^j       O>      ®       O    rfl 
U    ^     "C    '^    *O 


r^  -4->    d    K 

I  s  §  § 


H  S  •<  S 


POWER  AXD  ENERGY 


123 


FIG.  141. 
tion    of 


Illustra- 

potential 


energy 


is  lifted  from  the  first  position  in  Fig.  141  through  a  height 
of  1  m.  and  placed  upon  the  hook  H  at  the  end  of  a  cord 
which  passes  over  a  frictionless  pulley  p  and  is  attached  at 
the  other  end  to  a-second  kilogram  weight  B.  The  operation 
of  lifting  A  from  position  1  to  position  2  has 
required  an  expenditure  upon  it  of  1  kg.  m. 
(100,000  g.  cm.,  or  98,000,000  ergs)  of  work. 
But  in  position  2,  A  is  itself  possessed  of  a 
certain  capacity  for  doing  work  which  it  did 
not  have  before ;  for  if  it  is  now  started  down- 
ward by  the  application  of  the  slightest  con- 
ceivable force,  it  will,  of  its  own  accord,  return 
to  position  1,  and  will  in  so  doing  raise  the 
kilogram  \veight  B  through  a  height  of  1  m. 
In  other  words,  it  will  do  upon  B  exactly  the 
same  amount  of  work  that  was  originally 
done  upon  it. 

146.  Potential  and  kinetic  energy.  A  body  may  have  a 
capacity  for  doing  work  not  only  because  it  has  been  given  an 
elevated  position  but  also  because  it  has  in  some  way  acquired 
velocity ;  for  example,  a  heavy  flywheel  will  keep  machinery 
running  for  some  time  after  the  power  has  been  shut  off,  and 
a  bullet  shot  upward  will  lift  itself  a  great  distance  against 
gravity  because  of  the  velocity  which  has  been  imparted  to  it. 
Similarly,  any  body  which  is  in  motion  is  able  to  rise  against 
gravity,  or  to  set  other  bodies  in  motion  by  colliding  with  them, 
or  to  overcome  resistances  of  any  conceivable  sort.  Hence,  in 
order  to  distinguish  between  the  energy  which  a  body  may 
have  because  of  an  advantageous  position,  and  the  energy  which 
it  may  have  because  it  is  in  motion,  the  two  terms  "potential 
energy"  and  "kinetic  energy"  are  used.  Potential  energy 
includes  the  energy  of  lifted  weights,  of  coiled  or  stretched 
springs,  of  bent  bows,  etc.,  —  in  a  word,  potential  energy  is 
energy  of  position,  while  kinetic  energy  is  energy  of  motion. 


124  WORK  AND  MECHANICAL  ENERGY 

147.  Transformations  of  potential  and  kinetic  energy.    The 
swinging   of   a  pendulum    and   the   oscillation   of   a   weight 
attached  to  a  spring  illustrate  well  the  way  in  which  energy 
which  has  once  been  put  into  a  body  may  be  transformed 
back  and  forth  between  the  potential  and  kinetic  varieties. 
When  the  pendulum  bob  is  at  rest  at  the  bottom  of  its  arc, 
it  possesses  no  energy  of  either  type,  since,  on  the  one  hand, 
it  is  as  low  as  it  can  be,  and,  on  the  other,  it  has  no  velocity. 
When  we  pull  it  up  the  arc  to  the  posi- 
tion A  (Fig.  142),  we  do  an  amount 

of  work  upon  it  which  is  equal  in  gram 
centimeters  to  its  weight  in  grams 
times  the  distance  AD  in  centimeters  ; 
that  is,  we  store  up  in  it  this  amount 
of  potential  energy.  As  now  the  bob 
falls  to  C  this  potential  energy  is  com- 
pletely  transformed  into  kinetic  en- 
ergy. That  this  kinetic  energy  at  C  is 
exactly  equal  to  the  potential  energy  FIG.  142.  Transformation 

at  A  is  proved  by  the  fact  that  if  f ric-    of    P°tential   aild   kinetic 

GiiGr°*v 
tion  is  completely  eliminated,  the  bob 

rises  to  a  point  B  such  that  BE  is  equal  to  AD.  We  see, 
therefore,  that  at  the  ends  of  its  swing  the  energy  of  the 
pendulum  is  all  potential,  while  in  the  middle  of  the  swing 
its  energy  is  all  kinetic.  In  intermediate  positions  the  energy 
is  part  potential  and  part  kinetic,  but  the  sum  of  the  two  is 
equal  to  the  original  potential  energy. 

148.  General  statement  of  the  law  of  frictionless  machines. 
In  our  development  of  the  law  of  machines,  which  led  us  to  the 
conclusion  that  the  work  of  the  acting  force  is  always  equal  to 
the  work  of  the  resisting  force,  we  were  careful  to  make  two 
important   assumptions :    first,   that   friction   was  negligible ; 
second,  that  the  motions  were  all  either  uniform  or  so  slow 
that  no  appreciable  velocities  were  imparted.   In  other  words, 


POWER  AND  ENERGY  125 

we  assumed  that  the  work  of  the  acting  force  was  expended 
simply  in  lifting  weights  or  compressing  springs,  —  that  is, 
in  storing  up  potential  energy.  If  now  we  drop  the  second 
assumption,  a  very  simple  experiment  will  show  that  our  con- 
clusion must  be  somewhat  modified.  Suppose,  for  instance, 
that  instead  of  lifting  a  500-gram  weight  slowly  by  means  of  a 
balance,  we  jerk  it  up  suddenly.  We  shall  now  find  that  the 
initial  pull  indicated  by  the  balance,  instead  of  being  500  g., 
will  be  considerably  more,  —  perhaps  as  much  as  several  thou- 
sand grams  if  the  pull  is  sufficiently  sudden.  This  is  obviously 
because  the  acting  force  is  now  overcoming  not  merely  the 
500  g.  which  represents  the  resistance  of  gravity,  but  also  the 
inertia  of  the  body,  since  velocity  is  being  imparted  to  it.  Now 
work  done  in  imparting  velocity  to  a  body,  that  is,  in  over- 
coming its  inertia,  always  appears  as  kinetic  energy,  while  work 
done  in  overcoming  gravity  appears  as  the  potential  energy  of 
a  lifted  weight.  Hence,  whether  the  motions  produced  by 
machines  are  slow  or  fast,  if  friction  is  negligible  the  law  for 
all  devices  for  transforming  work  may  be  stated  thus:  The 
work  of  the  acting  force  is  equal  to  the  sum  of  the  potential  and 
kinetic  energies  stored  up  in  the  mass  acted  upon.  In  machines 
which  work  against  gravity  the  body  usually  starts  from  rest 
and  is  left  at  rest,  so  that  the  kinetic  energy  resulting  from  the 
whole  operation  is  zero.  Hence  in  such  cases  the  work  done  is 
the  weight  lifted  times  the  height  through  which  it  is  lifted, 
whether  the  motion  is  slow  or  fast.  The  kinetic  energy  im- 
parted to  the  body  in  starting  is  all  given  up  by  it  in  stopping. 
149.  The  measure  of  potential  energy.  The  measure  of  the 
potential  energy  of  any  lifted  body,  such  as  a  lifted  pile 
driver,  is  equal  to  the  work  which  has  been  spent  in  lifting 
the  body.  Thus,  if  h  is  the  height  in  centimeters  and  M  the 
weight  in  grams,  then  the  potential  energy  P.E.  of  the 
lifted  mass  is 

P.E.  =  Mh  gram  centimeters. 


126  WORK  AND  MECHANICAL  ENERGY 

Similarly,  if  h  is  the  height  in  feet,  and  M  the  weight  in 
pounds,  p  E  =  m  foot  pounds. 

150.  The  measure  of  kinetic  energy.  Since  the  force  of  the  earth's 
attraction  for  M  grams  is  Mg  dynes,  if  we  wish  to  express  the  potential 
energy  in  ergs  instead  of  in  gram  centimeters,  we  have 

P.E,  =  Mffh  ergs.  (12) 

Since  this  energy  is  all  transformed  into  kinetic  energy  when  the  mass 
falls  the  distance  h,  the  product  Mgh  also  represents  the  number  of  ergs 
of  kinetic  energy  which  the  moving  weight  has  when  it  strikes  the  pile. 

If  we  wish  to  express  this  kinetic  energy  in  terms  of  the  velocity  with 
which  the  weight  strikes  the  pile,  instead  of  the  height  from  which  it 
has  fallen,  we  have  only  to  substitute  for  h  its  value  in  terms  of  g  and 
the  velocity  acquired  (see  equation  (3),  p.  76),  namely  h  =  i?2/2  g.  This 
gives  the  kinetic  energy  K.E.  in  the  form 

K.E.  =  -i  J/y2  ergs.  (13) 

Since  it  makes  no  difference  how  a  body  has  acquired  its  velocity, 
this  represents  the  general  formula  for  the  kinetic  energy  in  ergs  of  any 
moving  body,  in  terms  of  its  mass  and  its  velocity. 

Thus,  the  kinetic  energy  of  a  100-gram  bullet  moving  with  a  velocity 
of  10,000  cm.  per  second  is 

K.E.  =  £  x  100  x  (10,000)2  =  5,000,000,000  ergs. 

Since  1  g.  cm.  is  equivalent  to  980  ergs,  the  energy  of  this  bullet  is 
5'ooy8°00'000  =  5,102,000  g.  cm.,  or  51.02  kg.  m. 

We  know,  therefore,  that  the  powder  pushing  on  the  bullet  as  it 
moved  through  the  rifle  barrel  did  51.02  kg.  m.  of  work  upon  the  bullet 
in  giving  it  the  velocity  of  100  m.  per  second. 

In  general  terms,  if  M  is  in  grams  and  v  in  centimeters  per  second, 

K.E.  =  ^  -  j^jr.  g.  cm.  ;  if  M  is  in  pounds  and  v  in  feet  per  second, 


QUESTIONS  AND  PROBLEMS 

1.  A  stick  of  dynamite  has  great  capacity  for  doing  work.    Before 
the  explosion  occurs,  is  the  energy  in  the  potential  or  the  kinetic  form  ? 

2.  Explain  the  use  of  the  sand  blast  in  cleaning  castings,  making 
frosted  glass,  cutting  figures  on  glassware,  cleaning  off  the  walls  of 
stone  buildings,  etc. 


POWER  AND  ENERGY  127 

3.  How  much  work  is  required  to  lift  the  500-pound  weight  of  a  pile 
driver  30  ft.?    How  much  potential  energy  is  then  stored  in  it?    How 
much  work  does  it  do  when  it  falls  ?   If  the  falling  mass  drives  the  pile 
into  the  earth  i  ft.,  what  is  its  average  force  upon  the  pile  ? 

4.  A  man  weighing  198  Ib.  walked  to  the  top  of  the  stairway  of  the 
Washington  Monument  (500  ft.  high)  in  10  min.  At  what  horse-power 
rate  did  he  work? 

5.  A  farm  tractor  drew  a  gang  plow  at  the  rate  of  2^  mi.  per  hour, 
maintaining  an  average  drawbar  pull  of  1500  Ib.    At  what  average  H.P. 
was  the  tractor  working  ? 

6.  In  the  course  of  a  stream  there  is  a  waterfall  22  ft.  high.  It  is 
shown  by  measurement  that  450  cu.  ft.  of  water  per  second  pours  over 
it.   How  many  foot  pounds  of  energy  per  second  could  be  obtained  from 
it?  What  horse  power? 

7.  How  many  gallons  of  water  (8  Ib.  each)  could  a  10-horse-power 
engine  raise  in  one  hour  to  a  height  of  60  f t.  ? 

8.  A  certain  airplane  using  three  400-horse-power  motors  flew  80  mi. 
per  hour.    With  how  many  pounds  backward  force  did  the  propellers 
push  against  the  air  ? 

9.  If  a  rifle  bullet  can  just  pass  through  a  plank,  how  many  planks 
will  it  pass  through  if  its  speed  is  doubled  ? 

10.  A  steel  ball  dropped  into  a  pail  of  moist  clay  from  a  height  of  a 
meter  sinks  to  a  depth  of  2  cm.    How  far  will  it  sink  if  dropped  4  in.  ? 

11.  Neglecting  friction,  find  how  much  force  a  boy  would  have  to 
exert  to  pull  a  100-pound  wagon  up  an  incline  which  rises  5  ft.  for 
every  100  ft.  of  length  traversed  on  the  incline.    In  addition  to  giving 
the  numerical  solution  of  the  problem,  state  why  you  solve  it  as  you  do 
and  how  you  know  that  your  solution  is  correct. 


CHAPTER  VIII 

THERMOMETRY ;    EXPANSION  COEFFICIENTS* 
THERMOMETBY 

151.  Meaning  of  temperature.   When  a  body  feels  hot  to  the 
touch  we  are  accustomed  to  say  that  it  has  a  high  temperature, 
and  when  it  feels  cold  that  it  has  a  low  temperature.   Thus  the 
word  "  temperature  "  is  used  to  denote  the  condition  of  hot- 
ness  or  coldness  of  the  body  whose  state  is  being  described. 

152.  Measurement  of  temperature.    So  far  as  we  know,  up 
to  the  time  of  Galileo  no  one  had  ever  used  any  special  instru- 
ment for  the  measurement  of  temperature.    People  knew  how 
hot  or  how  cold  it  was  from  their  feelings  only.    But  under 
some  conditions  this  temperature  sense  is  a  very  unreliable 
guide.     For  example,  if  the   hand   has   been  in   hot  water, 
tepid  water  will  feel   cold;    while   if   it  has   been   in   cold 
water,  the  same  tepid  water  will  feel  warm ;  a  room  may  feel 
hot  to  one  who  has  been  running,  while  it  will  feel  cool  to 
one  who  has  been  sitting  still. 

Difficulties  of  this  sort  have  led  to  the  introduction  in 
modern  times  of  mechanical  devices,  called  thermometers,  for 
measuring  temperature.  These  instruments  depend  for  their 
operation  upon  the  fact  that  almost  all  bodies  expand  as 
they  grow  hot. 

153.  Galileo's  thermometer.     It  was  in  1592  that  Galileo, 
at  the  University  of  Padua  in  Italy,  constructed   the  first 

*  It  is  recommended  that  this  chapter  be  preceded  by  laboratory  measure- 
ments on  the  expansions  of  a  gas  and  a  solid.  See,  for  example,  Experiments 
14  and  15  of  the  authors'  Manual. 

128 


THERMOMETRY 


129 


thermometer.  He  was  familiar  with  the  faots  of  expansion 
of  solids,  liquids,  and  gases ;  and  since  gases  expand  more 
than  solids  or  liquids,  he  chose  a  gas  as  his  expanding 
substance.  His  device  was  that  shown  in  Fig.  143. 

Let  a  bulb  of  air  B  be  connected  with  a  water  manometer  m,  as  in 
Fig.  143.  If  the  bulb  is  warmed  by  holding  a  Bunsen  burner  beneath 
it,  or  even  by  placing  the  hand  upon  it,  the  water 
at  m  will  at  once  begin  to  descend,  showing  that 
the  pressure  exerted  by  the  air  contained  in  the 
bulb  has  been  increased  by  the  increase  in  its 
temperature.  If  B  is  cooled  with  ice  or  ether,  the 
water  will  rise  at  m. 


FIG.  143.  Expansion 

of  air  by  heat 


154.  Significance  of  temperature  from  the 
standpoint  of  the  kinetic  theory.    Now  if,  as 
was  stated  in  §  64,  gas  pressure  is  due  to 
the  bombardment  of  the  walls  by  the  mole- 
cules of  the  gas,  since  the  number  of  mole- 
cules in  the  bulb  can  scarcely  have  been 
changed  by  slightly  heating  it  we  are  forced 
to  conclude  that  the  increase  in  pressure 

is  due  to  an  increase  in  the  velocity  of  the  molecules  which  are 
already  there.  From  the  standpoint  of  the  kinetic  theory  the 
pressure  exerted  by  a  given  number  of  molecules  of  a  gas  is 
determined  by  the  kinetic  energy  of  bombardment  of  these 
molecules  against  the  containing  walls.  To  increase  the  tem- 
perature is  to  increase  the  average  kinetic  energy  of  the  mole- 
cules, and  to  diminish  the  temperature  is  to  diminish  this 
average  kinetic  energy.  The  kinetic  theory  thus  furnishes  a 
very  simple  and  natural  explanation  of  the  fact  of  the  expan- 
sion of  gases  with  a  rise  in  temperature. 

155.  The  construction  of  a  centigrade  mercury  thermometer. 
It  was  not  until  about    1700   that   mercury   thermometers 
were   invented.    On   account  of   their   extreme   convenience 
these  have  now  replaced  all  others  for  practical  purposes. 


130     THERMOMETRY;  EXPANSION  COEFFICIENTS 


The  meaning  of  a  degree  of  temperature  change  as  measured 
by  a  mercury  thermometer  is  best  understood  from  a  descrip- 
tion of  the  method  of  making  and  graduating  the  thermometer. 

A  bulb  is  blown  at  one  end  of  a  piece  of  thick-walled 
glass  tubing  of  small,  uniform  bore.  Bulb  and  tube  are 
filled  with  mercury,  at  a  temperature  slightly  above  the 
highest  temperature  for  which  the  thermom- 
eter is  to  be  used,  and  the  tube  is  sealed 
off  in  a  hot  flame.  As  the 
mercury  cools,  it  contracts 
and  falls  away  from  the 
top  of  the  tube,  leaving  a 
vacuum  above  it. 

The  bulb  is  next  sur- 
rounded with  melting  snow 
or  ice,  as  in  Fig.  144,  and 
the  point  at  which  the  mer-  « 

cury  stands  in  the  tube  is 
marked  0°.    Then  the  bulb 
and  tube  are  placed  in  the 
steam    rising   from   boiling     FlG  144<  Method 
water  under  a  pressure  of     of  finding  the  0° 

76  cm.,  as  in  Fig.  145,  and     Point  in  calibrat- 
.  .  ing  a  thermometer 

the    new    position    or    the 

mercury  is  marked  100°.  The  space  between  these  two 
marks  011  the  stem  is  then  divided  into  100  equal  parts,  and 
divisions  of  the  same  length  are  extended  above  the  100° 
mark  and  below  the  0°  mark. 

One  degree  of  change  in  temperature,  measured  on  such  a 
thermometer,  means,  then,  such  a  temperature  change  as 
will  cause  the  mercury  in  the  stem  to  move  over  one  of 
these  divisions ;  that  is,  it  is  such  a  temperature  change  as 
will  cause  mercury  contained  in  a  glass  bulb  to  expand  y^  of 
the  amount  which  it  expands  in  passing  from  the  temperature 


FIG.  145.  Method 
of  finding  the  100° 
point  in  calibrat- 
ing a  thermometer 


THERMOMETRY 


131 


of  melting  ice  to  that  of  steam  under  a  pressure  of  76  cm. 
A  thermometer  in  which  the  scale  is  divided  in  this  way  is 
called  a  centigrade  thermometer. 

Thermometers  graduated  on  the  centigrade  scale  are  used 
almost  exclusively  in  scientific  work,  and  also  for  ordinary 
purposes  in  most  countries  which  have  adopted  the  metric 
system.  This  scale  was  first  devised  in  1742  by  Celsius,  of 
Upsala,  Sweden.  For  this  reason  it  is  sometimes  called  the 
Celsius  instead  of  the  centigrade  scale. 

According  to  the  kinetic  theory  an  increase  in  temperature  in 
a  liquid,  as  in  a  gas,  means  an  increase  in  the  mean  kinetic 
energy  of  the  molecules ;  and,  conversely,  a  decrease  in  tem- 
perature means  a  decrease  in  this  average  kinetic  energy. 

156.  Fahrenheit  thermometers.   The  com- 
mon household  thermometer  in  England  and 
the  United  States  differs  from  the  centigrade 
only  in  the  manner  of  its  graduation.    In  its 
construction  the  temperature  of  melting  ice 
is  marked  32°  instead  of  0°,  and  that  of  boil- 
ing water  212°  instead  of  100°.    The  inter- 
vening stem  is  then  divided  into  180  parts. 
The  zero  of  this  scale  is  the  temperature  ob- 
tained by  mixing  equal  weights  of  sal  ammo- 
niac  (ammonium  chloride)   and  snow.    In 
1714,  when  Fahrenheit  devised  this  scale,  he 
chose  this  zero  because  he  thought  it  repre- 
sented the  lowest  possible  temperature  that 
could  be  obtained  in  the  laboratory. 

157.  Comparison  of  centigrade  and  Fah- 
renheit thermometers.   From  the  methods  of 
graduation  of  the  Fahrenheit  and  centigrade 
thermometers  it  will  be  seen  that  100°  on 

the  centigrade  scale  denotes  the  same  difference  of  temper- 
ature as  180°  on  the  Fahrenheit  scale  (Fig.  146).  Hence  five 


FIG.  146.   The  cen- 
tigrade and  Fahren- 
heit scales 


132     THEEMOMETRY;  EXPANSION  COEFFICIENTS 


centigrade  degrees  are  equal  to  nine  Fahrenheit  degrees.    In 

Fig.  147,  C  represents  the  number  of  degrees  in  the  centigrade 

reading,  while  F  represents  the  number  in  the  Fahrenheit 

reading.    Since  five  centigrade  degrees  cover 

the  same  space  on  the  stem  as  nine  of  the 

smaller  Fahrenheit  degrees,  it  is  evident  that      ioo°Hllh2i2° 

C      ^5 

T^T  GO  Q 

By  this  expression  of  the  relation  of  the  two 
scales  it  is  very  easy  to  reduce  the  readings 
of  one  thermometer  to  the  scale  of  the  other. 
For  example,  to  find  what  Fahrenheit 
reading  corresponds  to  20°  C.  we  have 


FIG.  147.  Compari- 

158.  The  range  of  the  mercury  thermom-    son  of  centigrade  and 

C1.  „  OAO    _          Fahrenheit  scales 

eter.  Since  mercury  freezes  at  —  39  C., 
temperatures  lower  than  this  are  very  often  measured  by 
means  of  alcohol  thermometers,  for  the  freezing  point  of  alcohol 
is  —  130°  C.  Similarly,  since  the  boiling  point  of  mercury  is 
about  360°  C.,  mercury  thermometers  cannot  be  used  for 
measuring  very  high  temperatures.  For  both  very  high  and 
very  low  temperatures  —  in  fact,  for  all  temperatures  —  a  gas 
thermometer  is  the  standard  instrument. 

159.  The  standard  hydrogen  thermometer.    The  modern  gas 
thermometer  (Fig.  148)  is,  however,  widely  different  from  that 
devised  by  Galileo  (Fig.  143).    It  is  not  usually  the  increase 
in  the  volume  of  a  gas  kept  under  constant  pressure  which  is 
taken  as  the  measure  of  temperature  change,  but  rather  the  in- 
crease in  pressure  which  the  molecules  of  a  confined  gas  exert 
against  the  walls  of  a  vessel  whose  volume  is  kept  constant. 
The  essential  features  of  the  method  of  calibration  and  use 


THERMOMETRY 


133 


100°C 


o°c 


P373°A 


D273°A 


of  the  standard  hydrogen  thermometer  at  the  International 
Bureau  of  Weights  and  Measures  at  Paris  are  as  follows: 

The  bulb  B  (Fig.  148)  is  first  filled  with  hydrogen  and  the  space 
above  the  mercury  in  the  tube  a  made  as  nearly  a  perfect  vacuum  as 
possible.  B  is  then  surrounded  with  melting  ice 
(as  in  Fig.  144)  and  the  tube  a  raised  or  lowered 
until  the  mercury  in  the  arm  b  stands  exactly 
opposite  the  fixed  mark  c  on  the  tube.  Now, 
since  the  space  above  D  is  a  vacuum,  the  pressure 
exerted  by  the  hydrogen  in  B  against  the  mercury 
surface  at  c  just  supports  the  mercury  column 
ED.  The  point  D  is  marked  on  a  strip  of  metal 
behind  the  tube  a.  The  bulb  B  is  then  placed  in 
a  steam  bath  like  that  shown  in  Fig.  145.  The 
increased  pressure  of  the  gas  in  B  at  once  begins 
to  force  the  mercury  down  at  c  and  up  at  D. 
But  by  raising  the  arm  a  the  mercury  in  b  is 
forced  back  again  to  c,  the  increased  pressure  of 
the  gas  on  the  surface  of  the  mercury  at  c  being 
balanced  by  the  increased  height  of  the  mercury 
column  supported,  which  is  now  EF  instead  of 
ED.  When  the  gas  in  B  is  thoroughly  heated  to 
the  temperature  of  the  steam,  the  arm  a  is  very 
carefully  adjusted  so  that  the  mercury  in  b  stands 
very  exactly  at  c,  its  original  level.  A  second 
mark  is  then  placed  on  the  metal  strip  exactly 
opposite  the  new  level  of  the  mercury,  that  is,  at  F. 
Then  D  is  marked  0°  C.,  and  F  is  marked  100°  C. 
The  vertical  distance  between  these  marks  is  di- 
vided into  100  exactly  equal  parts.  Divisions  of 
exactly  the  same  length  are  carried  above  the 

100°  mark  and  below  'the  0°  mark.  One  degree  of  change  in  tempera- 
ture is  then  defined  as  any  change  in  temperature  which  will  cause  the 
pressure  of  the  gas  in  B  to  change  by  the  amount  represented  by  the 
distance  between  any  two  of  these  divisions.  This  distance  is  found  to 
be  2^  of  the  height  ED. 


-K  O'Aor 


FIG.  148.   The  stand- 
ard gas  thermometer 


In  other  words,  one  degree  of  change  in  temperature  on  the 
centigrade  scale  is  such  a  temperature  change  as  ivill  cause  the 


134     XHEBMOMETBY;  EXPANSION  COEFFICIENTS 

pressure  exerted  by  a  confined  volume  of  hydrogen  to  change  ly 
~-$  of  its  pressure  at  the  temperature  of  melting  ice  (0°  C.). 

160.  Absolute  temperature.    Since,  then,  cooling  the  hydro- 
gen through  1°  C.,  as  denned  above,  reduces  the  pressure  -^-^ 
of  its  value  at  0°  C/,  it  is  clear  that  cooling  it  278°  below  0°  C. 
would   reduce   its   pressure   to   zero.     But   from  the  stand- 
point of  the  kinetic  theory  this  would  be  the  temperature  at 
which  all  motions  of  the  hydrogen  molecules  would  cease. 
This  temperature  is  called  the  absolute  zero,  and  the  temper- 
ature measured  from  this  zero  is  called  absolute  temperature. 
Thus,  if  A  is  used  to  denote  the  absolute   scale,  we  have 
0°  C.  -  273°  A.,  100°  C.  =  373°  A.,  15°  C.  =  288°  A.,  etc.    It 
is  customary  to  indicate  temperatures  on  the  centigrade  scale 
by  £,  and  on  the  absolute  scale  by  T.    We  have,  then, 

T=£  +  273.  (1) 

161.  Comparison  of  gas  and  mercury  thermometers.    Since  an  inter- 
national committee  has  chosen  the  hydrogen  thermometer  described  in 
§  159  as  the  standard  of  temperature  measurement,  it  is  important  to 
know  whether  mercury  thermometers,  graduated  in  the  manner  described 
in  §  155,  agree  with  gas  thermometers  at  temperatures  other  than  0°  and 
100°  (where,  of  course,  they  must  agree,  since  these  temperatures  are  in 
each  case  the  starting  points  of  the  graduation).   A  careful  comparison 
has  shown  that  although  they  do  not  agree  exactly,  yet  fortunately  the 
disagreements  at  ordinary  temperatures  are  small,  not  amounting  to  more 
than  .2°  anywhere  between  0°  and  100°.  At  300°  C.,  however,  the  differ- 
ence amounts  to  about  4°.    (Mercury  thermometers  are  actually  used  for 
measuring  temperatures  above  the  boiling  point  of  mercury,  360°C.  They 
are  then  filled  with  nitrogen,  the  pressure  of  which  prevents  boiling.) 

Hence  for  all  ordinary  purposes  mercury  thermometers  are  sufficiently 
accurate,  and  no  special  standardization  of  them  is  necessary.  But  in 
all  scientific  work,  if  mercury  thermometers  are  used  at  all,  they  must 
first  be  compared  with  a  gas  thermometer  and  a  table  of  corrections 
obtained.  The  errors  of  an  alcohol  thermometer  are  considerably  larger 
than  those  of  a  mercury  thermometer. 

162.  Low  temperatures.    The  absolute  zero  of  temperature 
can,  of  course,  never  be  attained,  but  in  recent  years  rapid 


SIR  WILLIAM  THOMSON,  LORD  KELVIN  (1824-1907) 

One  of  the  best  known  and  most  prolific  of  nineteenth-century  physicists ;  born 
in  Belfast,  Ireland ;  professor  of  physics  in  Glasgow  University,  Scotland,  for 
more  than  fifty  years ;  especially  renowned  for  his  investigations  in  heat  and 
electricity ;  originator  of  the  absolute  thermodynamic  scale  of  temperature ; 
formulator  of  the  second  law  of  thermodynamics;  inventor  of  the  electrometer! 
the  mirror  galvanometer,  and  many  other  important  electrical  devices 


THERMOMETRY  135 

strides  have  been  made  toward  it.  Forty  years  ago  the  low- 
est temperature  which  had  ever  been  measured  was  —  110°  C., 
the  temperature  attained  by  Faraday  in  1845  by  causing  a 
mixture  of  ether  and  solid  carbon  dioxide  to  evaporate  in  a 
vacuum.  But  in  1880  air  was  first  liquefied  and  found,  by 
means  of  a  gas  thermometer,  to  have  a  temperature  of 
-190°C.  When  liquid  air  evaporates  into  a  space  which 
is  kept  exhausted  by  means  of  an  air  pump,  its  temperature 
falls  to  about  —  220°  C.  Recently  hydrogen  has  been  lique- 
fied and  found  to  have  a  temperature  at  atmospheric  pressure 
of  —  243°  C.  All  of  these  temperatures  have  been  measured 
by  means  of  hydrogen  thermometers.  By  allowing  liquid 
hydrogen  to  evaporate  into  a  space  kept  exhausted  by  an 
air  pump,  Dewar  in  1900  attained  a  temperature  of  —  260°. 
In  1911  Kamerlingh  Onnes  liquefied  helium  and  attained  a 
temperature  of  —  271.3°  C.,  only  1.7°  above  absolute  zero 
(see  §  217). 

QUESTIONS  AND  PROBLEMS 

1.  Define  0°C.  and  100°  C.    What  is  1°C.?  1°F.? 

2.  From  a  study  of  the  behavior  of  gases  we  conclude  that  there  is  a 
temperature  at  which  the  molecules  are  at  rest  and  at  which  bodies  there- 
fore contain  no  heat.    Give  the  reasoning  that  leads  to  this  conclusion. 

3.  Normal  room  temperature  is  68°  F.    What  is  it  centigrade? 

4.  The  normal  temperature  of  the  human  body  is  98. 6°  F.   What 
is  it  centigrade  ? 

5.  What  temperature  centigrade  corresponds  to  0°F.  ? 

6.  Mercury  freezes  at  about  —  40°  F.    What  is  this  centigrade  ? 

7.  The  temperature  of  liquid  air  is  —  190°  C.  What  is  it  Fahrenheit  ? 

8.  The  lowest  temperature  attainable  by  evaporating  liquid  helium 
is  -  271.3°  C.    What  is  it  Fahrenheit  ? 

9.  What  is  the  absolute  zero  of  temperature  on  the  Fahrenheit  scale  ? 

10.  Why  is  a  fever  thermometer  made  with  a  very  long  cylindrical 
bulb  instead  of  a  spherical  one  ? 

11.  When  the  bulb  of  a  thermometer  is  placed  in  hot  water,  it  at 
first  falls  a  trifle  and  then  rises.    Why  ? 

12.  How  does  the  distance  between  the  0°  mark  and  the  100°  mark 
vary  with  the  size  of  the  bore,  the  size  of  the  bulb  remaining  the  same  ? 

13.  What  is  meant  by  the  absolute  zero  of  temperature? 


136     THEEMOMETRY;  EXPANSION  COEFFICIENTS 

14.  Why  is  the  temperature  of  liquid  air  lowered  if  it  is  placed  under 
the  receiver  of  an  air  pump  and  the  air  exhausted  ? 

15.  Two  thermometers  have  bulbs  of  equal  size.    The  bore  of  one 
has  a  diameter  twice  that  of  the  other.    What  are  the  relative  lengths 
of  the  stems  between  0°  and  100°  ? 

EXPANSION  COEFFICIENTS 

163.  The  laws  of  Charles  and  Gay-Lussac.  When,  as  in  the 
experiment  described  in  §  159,  we  keep  the  volume  of  a  gas 
constant  and  observe  the  rate  at  which  the  pressure  increases 
with  the  rise  in  temperature,  we  obtain  the  pressure  coefficient  of 
expansion,  which  is  denned  as  the  ratio  between  the  increase  in 
pressure  per  degree  and  the  value  of  the  pressure  at  0°  C.  This 
was  first  done  for  different  gases  by  a  Frenchman,  Charles, 
in  1787,  who  found  that  the  pressure  coefficients  of  expansion  of 
all  gases  are  the  same.  This  is  known  as  the  law  of  Charles. 

When  we  arrange  the  experiment  so  that  the  gas  can  expand 
as  the  temperature  rises,  the  pressure  remaining  constant,  we 
obtain  the  volume  coefficient  of  expansion,  which  is  defined  as  the 
ratio  between  the  increase  in  volume  per  degree  and  the  total  vol- 
ume of  the  gas  at  0°  C.  This  was  first  done  for  different  gases  in 
1802  by  another  Frenchman,  Gay-Lussac,  who  found  that  all 
gases  have  the  same  volume  coefficient  of  expansion,  this  coefficient 
being  the  same  as  the  pressure  coefficient,  namely,  1/273.  This 
is  known  as  the  law  of  G-ay-Lussac. 

From  the  definition  of  absolute  temperature  and  from 
Charles's  law  we  learn  that,  for  all  gases  at  constant  volume, 
pressure  is  proportional  to  absolute  temperature ;  that  is, 

P       T 

=^  =  — '•  (2) 

^2     T, 

Also,  from  Gay-Lussac's  law  we  learn  that,  for  all  gases  at 
constant  pressure,  volume  is  proportional  to  absolute  temperature  ; 
that  is, 


EXPANSION  COEFFICIENTS  137 

If  pressure,  temperature,  and  volume  all  vary,*  we  have 

P  V      T 

fili-fi.  (4) 

P  V      T 

a    2         2 

Any  one  of  these  six  quantities  may  be  found  if  the  other 
five  are  known. 

If  the  volume  remains  constant,  that  is,  if  V1  =  V$  equation 
(4)  reduces  to  (2),  that  is,  to  Charles's  law.  If  the  pressure 
remains  constant,  PI  =  P2  and  equation  (4)  reduces  to  (3),  that 
is,  to  Gay-Lussac's  law.  If  the  temperature  does  not  change, 
T^  =  T2  and  equation  (4)  reduces  to  P^V^  =  P2V2<>  that  is,  to 

Boyle's  law.    If  the  ratio  of  densities  instead  of  volumes  is 

y  j) 

sought,  it  is  only  necessary  to  replace  —  in  (3)  and  (4)  by  — J. 

QUESTIONS  AND  PROBLEMS 

1.  Why  is  it  unsafe  to  let  a  pneumatic  inkstand  like  that  of  Fig.  30, 
p.  33,  remain  in  the  sun  ? 

2.  To  what  temperature  must  a  cubic  foot  of  gas  initially  at  0°  C. 
be  raised  in  order  to  double  its  volume,  the  pressure  remaining  constant? 

3.  If  the  volume  of  a  quantity  of  air  at  30°  C.  is  200  cc.,  at  what 
temperature  will  its  volume  be  300  cc.,  the  pressure  remaining  the  same? 

4.  If  the  air  within  a  bicycle  tire  is  under  a  pressure  of  2  atmospheres, 
that  is,  152  cm.  of  mercury,  when  the  temperature  is  10°  C.,  what  pressure 
will  exist  within  the  tube  when  the  temperature  changes  to  35°  C.? 

5.  If  the  pressure  to  which  15  cc.  of  air  is  subjected  changes  from 
76  cm.  to  40  cm.,  the  temperature  remaining  constant,  what  does  its 
volume  become  ?    (See  Boyle's  law,  p.  36.)    If,  then,  the  temperature  of 
the  same  gas  changes  from  15°  C.  to  100°  C.,  the  pressure  remaining 
constant,  what  will  be  the  final  volume  ? 

6.  The    air  within    a    half-inflated    balloon    occupies   a  volume   of 
100,000  1.    The  temperature  is  15°  C.  and  the  barometric  height  75  cm. 
What  will  be  its  volume  after  the  balloon  has  risen  to  the  height  of 
Mt.  Blanc,  where  the  pressure  is  37  cm.  and  the  temperature  —  10°  C.? 

*  If  this  is  not  clear  to  the  student,  let  him  recall  that  if  the  speeds  of  two 
runners  are  the  same,  then  their  distances  are  proportional  to  their  times, 
that  is,  -Dj/Da  =  t^/tz  ;  but  if  their  times  are  the  same  and  the  speeds  different, 
Dj/D-j  =  Sj/Sg.  If  now  one  runs  both  twice  as  fast  and  twice  as  long,  he  evi- 
dently goes  4  times  as  far;  that  is,  if  time  and  speed  both  vary,  D^D^  —  t 


138     THERMOMETRY;  EXPANSION  COEFFICIENTS 


EXPANSION  OF  LIQUIDS  AND  SOLIDS 

164.  The  expansion  of  liquids.    The  expansion  of  liquids 
differs  from  that  of  gases  in  that 

1.  The  coefficients  of  expansion  of  liquids  are  all  consider- 
ably smaller  than  those  of  gases. 

2.  Different  liquids  expand  at  wholly  different  rates ;  for 
example,  the  coefficient  of  alcohol  between  0°  and  10°  C.  is 
.0011 ;  of  ether  it  is  .0015 ;  of  petroleum,  .0009 ;  of  mercury, 
.000181. 

3.  The  same  liquid  often  has  different  coefficients  at  dif- 
ferent  temperatures ;    that   is,    the    expansion    is    irregular. 
Thus,  if  the  coefficient  of  alcohol  is  obtained  between  0°  and 
60°  C.,  instead  of  between  0°  and  10°  C.,  it  is  .0013  instead 
of  .0011. 

The  coefficient  of  mercury,  however,  is  very  nearly  constant 
through  a  wide  range  of  temperature,  which  indeed  might 
have  been  inferred  from  the  fact  that  mercury  thermometers 
agree  so  well  with  gas  thermometers. 

165.  Method  of  measuring  the  expansion  coeffi- 
cients of  liquids.    One  of  the  most  convenient 
and  common  methods  of  measuring  the  coeffi- 
cients of  liquids  is  to  place  them  in  bulbs  of 
known  volume,  provided  with  capillary  necks 
of  known  diameter,  like  that  shown  in  Fig.  149, 
and  then  to  watch  the  rise  of  the  liquid  in  the 
neck  for  a  given  rise  in  temperature.    A  certain 
allowance  must  be  made  for  the  expansion  of 
the  bulb,  but  this  can  readily  be  done  if  the 
coefficient    of  expansion   of   the   substance   of 
which  the  bulb  is  made  is  known. 

166.  Maximum    density    of    water.     When 

water  is  treated  in  the  way  described  in  the  preceding  para- 
graph, it  reaches  its  lowest  position  in  the  stem  at  4°  C.    As 


FIG.  149.   Bulb 
for    investigat- 
ing expansions 
of  liquids 


EXPANSION  OF  LIQUIDS  AND  SOLIDS         139 

the  temperature  falls  from  that  point  down  to  0°  C.,  water 
exhibits  the  peculiar  property  of  expanding  with  a  decrease  in 
temperature. 

We  learn,  therefore,  that  water  has  its  maximum  density  at 
a  temperature  of  4°  C. 

167.  The  cooling  of  a  lake  in  winter.    The  preceding  para- 
graph makes  it  easy  to  understand  the  cooling  of  any  large 
body  of  water  with  the   approach  of  winter.     The   surface 
layers   are   first   cooled   and   contract.      Hence,    being   then 
heavier  than  the  lower  layers,  they  sink  and  are  replaced 
by  the  warmer  water  from  beneath.    This  process  of  cooling 
at  the  surface,  and  sinking,  goes  on  until  the  whole  body  of 
water  has  reached  a  temperature  of  4°  C.    After  this  condi- 
tion has  been  reached,  further  cooling  of  the  surface  layers 
makes  them  lighter  than  the  water  beneath,  and  they  now 
remain  on  top  until  they  freeze.    Thus,  before  any  ice  what- 
ever can  form  on  the  surface  of  a  lake,  the  T^hole  mass  of 
water  to  the   very  bottom  must  be   cooled  to  4°  C.     This 
is  why  it  requires  a  much  longer  and  more  severe   period 
of  cold  to  freeze   deep   bodies  of  water  than   shallow  ones. 
Further,    since    the    circulation    described    above    ceases    at 
4°  C.,  practically  all  of  the  unfrozen  water  will  be  at  4°  C. 
even  in  the  coldest  .weather.     Only  the  water  which  is  in 
the  immediate  neighborhood  of  the  ice  will  be  lower  than 
4°  C.    This  fact  is  of  vital  importance  in  the  preservation  of 
aquatic  life. 

168.  Expansion  of  solids.   The  proofs  of  expansion  of  solids 
with  an  increase  in  temperature  may  be  seen  on  every  side. 
Railroad  rails  are  laid  with  spaces  between  their  ends  so  that 
they  may  expand  during  the  heat  of  summer  without  crowd- 
ing each  other  out  of  place.    Wagon  tires  are  made  smaller1 
than  the  wheels  which  they  are  to  fit.    They  are  then  heated 
until  they  become   large   enough  to  be   driven   on,   and  in 
cooling  they  shrink    again   and   thus  grip  the  wheels  with 


140     THERMOMETRY;  EXPANSION  COEFFICIENTS 

immense  force.     A  common   lecture-room  demonstration  of 
expansion  is  the  following: 

Lei  the  ball  B,  which  when  cool  just  slips  through  the  ring  7?,  be 
heated  in  a  Bunsen  flame.    It  will  now  be  found  too  large  to  pass 
through  the  ring ;  but  if  the  ring  is  heated,  or  if 
the  ball  is  again  cooled,  it  will  pass  through  easily 
(see  Fig.  150). 

If  the  expansion  of  gases  and  liquids  is  due 
to  the  increase  in  the  average  kinetic  energy 

»       .,    ,.          £  .-,     .          i        -,        ,-,      £  .  FIG.  150.  Expansion 

of  agitation  of  their  molecules,  the  foregoing  of  so]icls 

experiments  with    solids    must  clearly  be 
given  a  similar  interpretation.   In  a  word,  then,  the  temperature 
of  a  given  substance,  be  it  solid,  liquid,  or  gas,  is  determined 
by  the  average  kinetic  energy  of  agitation  of  its  molecules. 

169.  Linear  coefficients  of  expansion  of  solids.  It  is  often 
more  convenient  to  measure  the  increase  in  length  of  one 
edge  of  an  Expanding  solid  than  to  measure  its  increase  in 
volume.  The  ratio  between  the  increase  in  length  per  degree  rise 
in  temperature  and  the  total  length  is  called  the  linear  coeffi- 
cient of  expansion  of  the  solid.  Thus,  if  ll  represent  the  length 
of  a  bar  at  ^°,  and  12  its  length  at  £2°,  the  equation  which 
defines  the  linear  coefficient  k  is 


L  - 1 

L-l 


_2 


',(«,-*,) 


(5) 


The  linear  coefficients  of  a  few  common   substances  are 
given    in   the    following    table : 

Aluminium  .  .000023  Gold 000014  Silver     .    .    .    .000019 

Brass      .    .  .  .000019  Iron 000012  Steel 000013 

Copper  .    .  .  .000017  Lead 000029  Tin 000023 

Glass .  .000009  Platinum    .    .    .000009  Zinc 000030 


APPLICATIONS  OF  EXPANSION 


141 


APPLICATIONS  OF  EXPANSION 

170.  Compensated  pendulum.    Since  a  long  pendulum  vi- 
brates more  slowly  than  a  short'  one,  the  expansion  of  the 
rod   which   carries   the   pendulum   bob   causes    an   ordinary 
clock  to  run  too    slowly  in  summer,  and 

its  contraction  causes  it  to  run  too  fast 
in  winter.  For  this  reason  very  accurate 
clocks  are  provided  with  compensated  pen- 
dulums, which  are  so  constructed  that  the 
distance  of  the  bob  beneath  the  point  of 
support  is  independent  of  the  temperature. 
This  is  accomplished  by  suspending  the  bob, 
by  means  of  two  sets  of  rods  of  different 
material,  in  such  a  way  that  the  expansion 
of  one  set  raises  the  bob,  while  the  expan- 
sion of  the  other  set  lowers  it.  Such  a 
pendulum  is  shown  in  Fig.  151.  The  ex-  FlG 
pansion  of  the  iron  rods  6,  c?,  e,  and  i  tends  pensated  pendulum 
to  lower  the  bob,  while  that  of  the  copper 
rods  c  tends  to.  raise  it.  In  order  to  produce  complete  com- 
pensation it  is  only  necessary  to  make  the  total  lengths  of 
iron  and  copper  rods  inversely  proportional  to  the  coefficients 
of  expansion  of  iron  and  copper. 

171.  Compensated  balance  wheel.    In 
the  balance  wheel  of  an  accurate  watch 
(Fig.  152)    another   application    of  the 
unequal  expansion  of  metals  is  made. 
Increase  in  temperature  both  increases 

the  radius   of  the  wheel   and  weakens     _, 

FIG.  152.   The  compen- 

the  elasticity  of   the  spring  which  con-        sated  balance  wheel 
trols  it.    Both  of  these  effects  tend  to 
make  the  watch  lose  time.    This  tendency  may  be  counter- 
acted by  bringing  the  mass  of  the  rotating  parts  in  toward 


The  com_ 


142     THEBMOMETRY;  EXPANSION  COEFFICIENTS 

the  center  of  the  wheel.    This  is  accomplished  by  making  the 
arcs  be  of  metals  of  different  expansion  coefficients,  the  inner 


FIG. 153  FIG. 154 

Unequal  expansion  of  metals 

metal,  shown  in  black  in  the  figure,  having  the  smaller  coeffi- 
cient.    The  free  ends  of  the  arcs  are  then  sufficiently  pulled 

in  by  a  rise  in  temperature  to  counteract  the 

retarding  effects. 

The  principle  is  precisely  the  same  as  that  which 
finds  simple  illustration  in  the  compound  bar  shown 
in  Fig.  153.  This  bar  consists  of  two  strips, 
one  of  brass  and  one  of  iron,  riveted  to- 
gether.  When  the  bar  is  placed  edgewise 
in  a  Bunsen  flame,  so  that  both  metals  are 
heated  equally,  it  will  be  found  to  bend  in 
such  a  way  that  the  more  expansible  metal, 
namely,  the  brass,  is  on  the  outside  of  the 
curve,  as  shown  in  Fig.  154.  When  it  is 
cooled  with  snow  or  ice,  it  bends  in  the 
opposite  direction. 

The  common  thermostat  (Fig.  155)  is 
precisely  such  a  bar,  which  is  arranged  so 
as  to  open  the  drafts  by  closing  an  electri- 
cal circuit  at  a  when  it  is  too  cold,  and  to  close  the  drafts 
by  making  contact  at  b  when  it  is  too  warm. 


FIG.  155.   The 

thermostat 


QUESTIONS  AND  PROBLEMS 


FIG.  156 


1.  Why  is  the  water  at  the  bottom  of  a  lake  usually  colder  than  that 
at  the  top  ?  Why  is  the  water  at  the  bottom  of  very  deep  mountain  lakes 
in  some  instances  observed  to  be  at  4°  C.  the  whole  year  round,  while 
that  at  the  top  varies  from  0°  C.  to  quite  warm  ? 

2.  Give  three  reasons  why  mercury  is  a  better  liquid  to  use  in  ther- 
mometers than  water. 

3.  Why  is  a  thick  tumbler  more  likely  to  break  when  hot  water  is 
poured  into  it  than  a  thin  one  ? 


APPLICATIONS  OF  EXPANSION  143 

4.  Pendulums  are  often  compensated  by  using  cylinders  of  mercury, 
as  in  Fig.  156.    Explain. 

5.  The  steel  cable  from  which  Brooklyn  Bridge  hangs  is  more  than 
a  mile  long.    By  how  many  feet  does  a  mile  of  its  length  vary  between 
a  winter  day  when  the  temperature  is  —  20°  C.  and 

a  summer  day  when  it  is  30°  C.  ? 

6.  If  a  surveyor's  steel  tape  is  exactly  100  ft. 
long  at  20°  C.,  how  much  too  short  would  it  be 
at  0°  C.  ? 

7.  A  certain  glass  flask  is  graduated  to  hold 
1000  cc.  at  15°  C.    How  many  cubic  centimeters 
will  the  same  flask  hold  at  40°  C.,  the  coefficient 
of  cubical  expansion  of  glass  being  .000025  ? 

8.  The  dial  thermometer  is  a  compound  bar  (Fig.  157)  with  iron  on 
the  outside  and  brass  on  the  inside.    A  thread  t  is  wound  about  the 
central  cylinder  c.    Explain  the  action. 

9.  Why  may  a  glass  stopper  sometimes  be  loosened  by  pouring  hot 
water  on  the  neck  of  a  bottle  ? 

10.  A  metal  rod  230  cm.  long  expanded  2.75  mm.  in  being  raised 
from  0°C.  to  100°C.    Find  its  coefficient  of  linear  expansion. 

11.  The  changes  in  temperature  to  which  long  lines  of  steam  pipes 
are  subjected  make  it  necessary  to  introduce  "expansion  joints."    These 
joints  consist  of  brass  collars  fitted  tightly  by  means  of  packing  over 
the  separated  ends  of  two  adjacent  lengths  of  pipe.   If  the  pipe  is  of 
iron,  and  such  a  joint  is  inserted  every  200  ft.,  and  if  the  range  of  tem- 
perature which  must  be  allowed  for  is  from  —  30° C.  to  125° C.,  what  is 
the  minimum  play  which  must  be  allowed  for  at  each  expansion  joint  ? 

12.  Show  from  equation  5,  p.  140,  that  linear  coefficient  of  expansion 
may  be  defined  as  increase  in  length  per  unit  length  per  degree. 


CHAPTER  IX 

WORK  AND  HEAT  ENERGY 
FRICTION 

172.  Friction  always  results  in  wasted  work.  All  of  the 
experiments  mentioned  in  Chapter  VII  were  so  arranged 
that  friction  could  be  neglected  or  eliminated.  So  long  as 
this  condition  was  fulfilled  it  was  found  that  the  result  of 
universal  experience  could  be  stated  thus :  The  work  done  by 
the  acting  force  is  equal  to  the  sum  of  the  kinetic  and  potential 
energies  stored  up. 

But  wherever  friction  is  present  this  law  is  found  to  be 
inexact,  for  the  work  of  the  acting  force  is  then  always 
somewhat  greater  than  the  sum  of  the  kinetic  and  potential 
energies  stored  up.  If,  for  example,  a  block  is  pulled  over 
the  horizontal  surface  of  a  table,  at  the  end  of  the  motion 
no  velocity  has  been  imparted  to  the  block,  and  hence  no 
kinetic  energy  has  been  stored  up.  Further,  the  block  has 
not  been  lifted  nor  put  into  a  condition  of  elastic  strain, 
and  hence  no  potential  energy  has  been  communicated  to  it. 
We  cannot  in  any  way  obtain  from  the  block  more  work 
after  the  motion  than  we  could  have  obtained  before  it  was 
moved.  It  is  clear,  therefore,  that  all  of  the  work  which 
was  done  in  moving  the  block  against  the  friction  of  the 
table  was  wasted  work.  Experience  shows  that,  in  general, 
where  work  is  done  against  friction  it  can  never  be  regained. 
Before  considering  what  becomes  of  this  wasted  work  we 
shall  consider  some  of  the  factors  on  which  friction  depends 
and  some  of  the  laws  which  are  found  by  experiment  to 
hold  in  cases  in  which  friction  occurs. 

144 


FRICTION 


145 


173.  Coefficient  of  friction.  It  is  found  that  if  F  represents 
the  force  parallel  to  a  plane  which  is  necessary  to  maintain 
uniform  motion  in  a  body  which  is  pressed  against  the  plane 
with  a  force  F',  then,  for  small  F=300 

velocities,  the   ratio  —  depends 

only  on  the  nature  of  the  surfaces 

in  contact,  and  not  at  all  on  the  FIG.  158.  The  ratio  of  FtoF'  is 

area    or  on  the  velocity  of  the         the  coefficient  of  friction 

77T 

motion.    The  ratio  —  is  called  the  coefficient  of  friction  for 
F 

the  given  materials.    Thus  (Fig.  158),  if  F  is  300  g.  and  F' 

goo—  •«•«'•    The  coeffi- 


is  800  g.,  the  coefficient  of  friction  is  MS  =  -375. 


cient  of  iron  on  iron  is  about  .2 ;  of  oak  on  oak,  about  .4. 

174.  Rolling  friction.  The  chief  cause  of  sliding  friction  is  the  inter- 
locking of  minute  projections.  When  a  round  solid  rolls  over  a  smooth 
surface,  the  frictional  resistance  is  generally  much  less  than  when  it 
slides ;  for  example,  the  coefficient  of  friction  of  cast-iron  wheels  rolling 
on  iron  rails  may  be  as  low  as  .002,  that  is,  y^  of  the  sliding  friction 

(1)  (2) 


FIG.  159.    Friction  in  bearings 
(1)  Common  bearing ;  (2)  ball  bearing 

of  iron  on  iron.  This  means  that  a  pull  of  1  pound  will  keep  a  500- 
pound  car  in  motion.  Sliding  friction  is  not,  however,  entirely  dis- 
pensed with  in  ordinary  wheels,  for  although  the  rim  of  the  wheel  rolls 
on  the  track,  the  axle  slides  continuously  at  some  point  c  (Fig.  159, 
(1))  upon  the  surface  of  the  journal.  Journals  are  frequently  lined  with 
brass  or  Babbitt  metal,  since  this  still  further  lowers  the  coefficient. 

The  great  advantage  of  the  ball  bearing  (Fig.  159,  (2))  is  that  the 
sliding  friction  in  the  hub  is  almost  completely  replaced  by  rolling 
friction.  The  manner  in  which  ball  bearings  are  used  in  a  bicycle 


146 


WORK  AND  HEAT  ENERGY 


pedal  is  illustrated  in  Fig.  160.    The  free-wheel  ratchet  ia  shown  in 
Fig.  161.    The  pawls  a  and  b  enable  the  pedals  and  chain  wheel  W  to 
stop  while  the  rear  axle  continues  to  revolve.  Roller  bearings  are  showD 
in  Fig.  162.   Oils  and  greases  prevent  rapid 
wear   of   bearings    by   lessening    friction. 


FIG.  160.   The  bicycle  pedal 


FIG.  161.   Free-wheel  ratchet 


175.  Fluid  friction.  When  a  solid  moves  through  a  fluid,  as  when  a 
bullet  moves  through  the  air  or  a  ship  through  the  water,  the  resistance 
encountered  is  not  at  all  independent  of  velocity,  as  in  the  case  of  solid 
friction,  but  increases  for  slow  speeds  nearly  as 
the  square  of  the  velocity,  and  for  high  speeds  at 
a  rate  considerably  greater.  This  explains  why 
it  is  so  expensive  to  run  a  fast  train ;  for  the  re- 
sistance of  the  air,  which  is  a  small  part  of  the 
total  resistance  so  long  as  the  train  is  moving 
slowly,  becomes  the  predominant  factor  at  high 
speeds.  The  resistance  offered  to  steamboats 
running  at  high  speeds  is  usually  considered  to 
increase  as  the  cube  of  the  velocity.  Thus,  the 
Cedric,  of  the  White  Star  Line,  having  a  speed  of 
17  knots,  has  a  horse  power  of  14,000  and  a  total 
weight,  when  loaded,  of  about  38,000  tons,  while 
the  Mauretania,  of  the  Cunard  Line,  having  a 
speed  of  25  knots,  has  engines  of  70,000  horse 
power,  although  the  total  weight  when  loaded  is 
only  32,500  tons. 

QUESTIONS  AND  PROBLEMS 

1.  Mention  three  ways  of  lessening  friction  in  machinery. 

2.  In  what  respects  is  friction  an  advantage,  and  in  what  a  disadvan- 
tage, in  everyday  life  ?    Could  we  get  along  without  it  ? 

3.  Why  is  a  stream  swifter  at  the  center  than  at  the  banks  ? 

4.  Why  does  a  team  have  to  keep  pulling  after  a  load  is  started? 


FIG.  162.    Roller   bear- 
ings of  automobile  front 
wheel 


EFFICIENCY  147 

5.  Why  is  sand  often  placed  on  a  track  in  starting  a  heavy  train  ? 

6.  In  what  way  is  friction  an  advantage  in  lifting  buildings  with  a 
jackscrew  ?    In  what  way  is  it  a  disadvantage  ? 

7.  A  smooth  block  is  10  x  8  x  3  in.    Compare  the  distances  which  it 
will  slide  when  given  a  certain  initial  velocity  on  smooth  ice  if  resting 
first,  on  a  10  x  8  face ;  second,  on  a  10  x  3  face  ;  third,  on  an  8  x  3  face. 

8.  What  is  the  coefficient  of  friction  of  brass  on  brass  if  a  force  of 
25  Ib.  is  required  to  maintain  uniform  motion  in  a  brass  block  weighing 
200  Ib.  when  it  slides  horizontally  on  a  brass  bed  ? 

9.  The  coefficient  of  friction  between  a  block  and  a  table  is  .3.    What 
force  will  be  required  to  keep  a  500-gram  block  in  uniform  motion  ? 

EFFICIENCY 

176.  Definition  of  efficiency.    Since  it  is  only  in  an  ideal 
machine  that  there  is  no  friction,  in  all  actual  machines  the 
work  clone  by  the  acting  force  always  exceeds,  by  the  amount 
of  the  work  done  against  friction,  the  amount  of  potential 
and  kinetic  energy  stored  up.    We  have  seen  that  the  former 
is  wasted  work  in  the  sense  that  it  can  never  be  regained. 
Since  the  energy  stored  up  represents  work  which  can  be 
regained,  it  is  termed  useful  work.    In  most  machines  an  effort 
is   made   to    have   the   useful   work    as    large   a  fraction   of 
the  total  work  expended  as  possible.    The  ratio  of  the  useful 
work  to  the  total  work  done  by  the  acting  force  is  called  the 
EFFICIENCY  of  the  machine.    Thus 

Useful  work  accomplished 

Efficiency  =  — ™-— r-  ^n C1) 

lotal  work  expended 

Thus,  if  in  the  system  of  pulleys  shown  in  Fig.  116  it  is  necessary  to 
add  a  weight  of  50  g.  at  E  in  order  to  pull  up  slowly  an  added  weight  of 
240  g.  at  7t,  the  work  done  by  the  50  g.  while  E  is  moving  over  1  cm. 
will  be  50  x  1  g.  cm.  The  useful  work  accomplished  in  the  same  time 

1  240  x  1      4 

is  240  x  —  g.  cm.    Hence  the  efficiency  is  equal  to  — *•  =  —  =  80%. 

o  50  x  1        o 

177.  Efficiencies  of  some  simple  machines.    In  simple  levers 
the  friction  is  generally  so  small  as  to  be  negligible  ;  hence  the 
efficiency  of  such  machines  is  approximately  100%.    When 


148 


WORK  AND  HEAT  ENERGY 


inclined  planes  are  used  as  machines,  the  friction  is  also  small, 
so  that  the  efficiency  generally  lies  between  90%  and  100%. 
The  efficiency  of  the  commercial  block  and  tackle  (Fig.  116), 
with  several  movable  pulleys,  is  usually  considerably  less, 
varying  between  40%  and  60%.  In  the  jackscrew  there  is 
necessarily  a  very  large  amount  of  friction,  so  that  although 
the  mechanical  advantage  is  enormous,  the  efficiency  is  often 
as  low  as  25%.  The  differential  pulley  of  Fig.  136  has  also  a 
very  high  mechanical  advantage  with  a  very  small  efficiency. 
Gear  wheels  such  as  those  shown  in  Fig.  134,  or  chain  gears 
such  as  those  used  in  bicycles,  are  machines  of  comparatively 
high  efficiency,  often  utilizing  between  90%  and  100%  of 
the  energy  expended  upon  them. 

178.  Efficiency  of  overshot  water  wheels.    The  overshot  water  wheel 
(Fig.  163)  utilizes  chiefly  the  potential  energy  of  the  water  at  S,  for 
the  wheel  is  turned  by  the  weight  of  the 

water  in  the  buckets.   The  work  expended 

on  the  wheel  per  second,  in  foot  pounds  or 

gram  centimeters,   is  the   product   of  the 

weight  of  the  water  which  passes  over  it 

per  second  by  the  distance  through  which 

it  falls.    The  efficiency  is  the  work  which 

the  wheel    can    accomplish    in    a    second 

divided    by    this    quantity.     Such    wheels 

are  very  common  in  mountainous  regions, 

where  it  is  easy  to  obtain  considerable  fall 

but  where  the  streams  carry  a  small  volume 

of  water.   The  efficiency  is  high,  being  often 

between  80  %  and  90  %.   The  loss  is  due  not 

only  to  the  friction  in  the  bearings  and 

gears  (see  C)  but  also  to  the  fact  that  some 

of  the  water  is  spilled  from  the  buckets  or  passes  over  without  entering 

them  at  all.    This  may  still  be  regarded  as  a  frictional  loss,  since  the 

energy  disappears  in  internal  friction  when  the  water  strikes  the  ground. 

179.  Efficiency  of  undershot  water  wheels.    The  old-style  undershot 
wheel  (Fig.  164)  — so  common  in  flat  countries,  where  there  is  little  fall 
but  an  abundance  of  water — utilizes  only  the  kinetic  energy  of  the  water 


FIG.  163.   Overshot  water 
wheel 


EFFICIENCY 


149 


FIG.  164.   The  undershot 
wheel 


running  through  the  race  from  ,-1.  It  seldom  transforms  into  useful 
work  more  than  25%  or  30%  of  the  potential  energy  of  the  water  above 
the  dam.  There  are,  however,  certain  mod- 
ern forms  of  undershot  wheel. which  are 
extremely  efficient.  For  example,  the  Pelton 
icheel  (Fig.  165),  developed  since  1880  and 
now  very  commonly  used  for  small-power 
purposes  in  cities  supplied  with  waterworks, 
sometimes  has  an  efficiency  as  high  as  83  %. 
The  water  is  delivered  from  a  nozzle  0 
against  cup-shaped  buckets  arranged  as  in 
the  figure.  At  the  Big  Creek  development 

in  California,  Pelton  wheels  94  inches  in  diameter  are  driven  by  water 
coming  with  a  velocity  of  350  feet  per  second  (how  many  miles  per 
hour?)  through  nozzles  6  inches  in  diameter.  The  head  of  water  is 
here  1900  ft. 

180.  Efficiency  of  water  turbines.  The 
turbine  wheel  was  invented  in  France  in 
1833  and  is  now  used  more  than  any 
other  form  of  wrater  wheel.  It  stands 
completely  under  water  in  a  case  at  the 
bottom  of  a  turbine  pit,  rotating  in  a  hori- 
zontal plane.  Fig.  166  shows  the  method 
of  installing  a  turbine  at  Niagara.  C  is 
the  outer  case  into  which  the  water  enters 
from  the  penstock  p.  Fig.  167,  (1),  shows 
the  outer  case  with  contained  turbine ; 
Fig.  167,  (2),  is  the  inner  case,  in  which 
are  the  fixed  guides  G,  which  direct  the 

water  at  the  most  advantageous  angle  against  the  blades  of  the  wheel 
inside ;  Fig.  167,  (3),  is  the  wheel  itself ;  and  Fig.  167,  (4),  is  a  section 
of  wheel  and  inner  case,  showing  how  the  water  enters  through  the 
guides  and  impinges  upon  the  blades  W.  The  spent  water  simply 
falls  down  from  the  blades  into  the  tailrace  T  (Fig.  166).  The  amount 
of  water  which  passes  through  the  turbine  can  be  controlled  by  means 
of  the  rod  P  (Fig.  167,  (1)),  which  can  be  turned  so  as  to  increase  or 
decrease  the  size  of  the  openings  between  the  guides  G  (Fig.  167,  (2)). 
The  energy  expended  upon  the  turbine  per  second  is  the  product  of 
the  mass  of  water  which  passes  through  it  by  the  height  of  the  turbine 
pit.  Efficiencies  as  high  as  90  %  have  been  attained  with  such  wheels. 


FIG.  165.   The  Pelton  water 
wheel 


150 


WORK  AND  HEAT  ENERGY 


One  of  the  largest  turbines  in  existence  is  operated  by  the  Puget  Sound 
Power  Co.  It  develops  25,000  horse  power  under  a  440-foot  head  of  water. 


FIG.  166.   A  turbine 
installed 


FIG.  167.   The  turbine  wheel 

(1)  Outer  case ;    (2)  inner  case ;    (3)  rotating 
part ;  (4)  section 


QUESTIONS  AND  PROBLEMS 

1 .  Why  is  the  efficiency  of  the  jackscrew  low  and  that  of  the  lever  high  ? 

2.  Find  the  efficiency  of  a  machine  in  which  an  effort  of  12  Ib. 
moving  5  ft.  raises  a  weight  of  25  Ib.  2  ft. 

3.  What  amount  of  work  was  done  on  a  block  and  tackle  having  an 
efficiency  of  60  %  when  by  means  of  it  a  weight  of  750  Ib.  was  raised  50  ft.  ? 

4.  A  force  pump  driven  by  a  1-horse-power  engine  lifted  4  cu.  ft.  of 
water  per  minute  to  a  height  of  100  ft.    What  was  the  efficiency  of  the 
pump? 

5.  If  it  is  necessary  to  pull  on  a  block  and  tackle  with  a  force  of 
100  Ib.  in  order  to  lift  a  weight  of  300  Ib.,  and  if  the  force  must  move 
6  ft.  to  raise  the  weight  1  ft.,  what  is  the  efficiency  of  the  system  ? 


MECHANICAL  EQUIVALENT  OF  HEAT          151 

6.  If  the  efficiency  had   been  65%,  what  force  would  have  been 
necessary  in  the  preceding  problem  ? 

7.  The  Niagara  turbine  pits  are  136  ft.  deep,  and  their  average  horse 
power  is  5000.    Their  efficiency  is  85%.    How  much  water  does  each 
turbine  discharge  per  minute? 

MECHANICAL  EQUIVALENT  OF  HEAT  * 

181.  What  becomes  of  wasted  work  ?  In  all  the  devices  for 
transforming  work  which,  we  have  considered  we  have  found 
that  on  account  of  frictional  resistances  a  certain  per  cent  of 
the  work  expended  upon  the  machine  is  wasted.  The  question 
which  at  once  suggests  itself  is,  What  becomes  of  this  wasted 
work  ?  The  following  familiar  facts  suggest  an  answer.  When 
two  sticks  are  vigorously  rubbed  together,  they  become  hot ;. 
augers  and  drills  often  become  too  hot  to  hold ;  matches  are 
ignited  by  friction ;  if  a  strip  of  lead  is  struck  a  few  sharp 
blows  with  a  hammer,  it  is  appreciably  warmed.  Now,  since 
we  learned  in  Chapter  VIII  that,  according  to  modern  notions, 
increasing  the  temperature  of  a  body  means  simply  increasing 
the  average  velocity  of  its  molecules,  and  therefore  their  average 
kinetic  energy,  the  above  facts  point  strongly  to  the  conclu- 
sion that  in  each  case  the  mechanical  energy  expended  has  been 
simply  transformed  into  the  energy  of  molecular  motion.  This 
view  was  first  brought  into  prominence  in  1798  by  Benjamin 
Thompson,  Count  Rumford,  an  American  by  birth,  who  was 
led  to  it  by  observing  that  in  the  boring  of  cannon  heat  was 
continuously  developed.  It  was  first  carefully  tested  by  the 
English  physicist  James  Prescott  Joule  (see  opposite  p.  122) 
(1818-1889)  in  a  series  of  epoch-making  experiments  extend- 
ing from  1842  to  1870.  In  order  to  understand  these  experi- 
ments we  must  first  learn  how  heat  quantities  are  measured. 

*  This  subject  should  be  preceded  by  a  laboratory  experiment  upon  the 
"law  of  mixtures,"  and  either  preceded  or  accompanied  by  experiments 
upon  specific  heat  and  mechanical  equivalent.  See  authors'  Manual,  Exper- 
iments 18,  19,  and  20. 


152  WORK  AND  HEAT  ENERGY 

182.  Units  of  heat ;  the  calorie  and  the  British  thermal 
unit.  The  calorie  is  the  amount  of  heat  that  is  required  to 
raise  the  temperature  of  1  gram  of  water  through  1°  (,"'.,  and 
the  British  thermal  unit  {B.  T.  Z7.)  is  the  amount  of  heat  that 
is  required  to  raise  the  temperature  of  1  pound  of  water 
through  1°  F.  (One  B.T.U.  =  252  cal.)  Thus,  when  a  hun- 
dred grams  of  water  has  its  temperature  raised  4°  C.  we  say 
that  four  hundred  calories  of  heat  have  entered  the  water. 
Similarly,  when  a  hundred  grams  of  water  has  its  temperature 
lowered  10°  C.  we  say  that  a  thousand  calories  have  passed  out 
of  the  water.  If,  then,  we  wish  to  measure,  for  instance,  the 
amount  of  heat  developed  in  a  lead  bullet  when  it  strikes 
against  a  target,  we  have  only  to  let  the  spent  bullet  fall  into 
a  known  weight  of  water  and  to  measure  the  number  of 
degrees  through  which  the  temperature  of  the  w^ater  rises. 
The  product  of  the  number  of  grams  of  wrater  by  its  rise  in 
temperature  is,  then,  by  definition,  the  number  of  calories  of 
heat  which  have  passed  into  the  water. 

It  will  be  noticed  that  in  the  above  definition  we  maive 
no  assumption  whatever  as  to  what  heat  is.  Previous  to  the 
nineteenth  century  physicists  generally  held  it  to  be  an 
invisible,  weightless  fluid,  the  passage  of  which  into  or  out 
of  a  body  caused  it  to  grow  hot  or  cold.  This  view  accounts 
well  enough  for  the  heating  which  a  body  experiences  when 
it  is  held  in  contact  with  a  flame  or  other  hot  body,  but  it 
has  difficulty  in  explaining  the  heating  produced  by  rubbing 
or  pounding.  Rumford's  view  accounts  easily  for  this,  as  we 
have  seen,  while  it  accounts  no  less  easily  for  the  heating  of 
cold  bodies  by  contact  with  hot  ones;  for  we  have  only  to 
think  of  the  hotter  and  therefore  more  energetic  molecules 
of  the  hot  body  as  communicating  their  energy  to  the  mole- 
cules of  the  colder  body  in  much  the  same  way  in  which  a 
rapidly  moving  billiard  ball  transfers  part  of  its  kinetic  energy 
to  a  more  slowly  moving  ball  against  which  it  strikes. 


©  Underwood  &  Underwood 

THE  ViCKERS-ViMY  AIRPLANE 

The  first  nonstop  transatlantic  airplane  flight  was  made  on  June  14,  1919,  from 
St.  John's,  Newfoundland,  to  Clifden,  Ireland,— a  distance  of  1890  miles.  This 
historic  flight  —  the  longest  ever  made — was  accomplished  in  fifteen  hours  and 
fifty-seven  minutes,  through  fog  and  sleet,  at  an  average  speed  of  118.5  miles  per 
hour,  —  a  feat  which  won  the  $50,000  prize  which  had  been  offered  for  nearly  five 
years  by  the  London  Daily  Mail.  The  plane  was  driven  by  two  360-horse-power 
Rolls-Royce  motors  and  carried  865  gallons  of  gasoline.  It  was  piloted  by  Capt. 
John  Alcock  and  navigated  by  Lieut.  Arthur  W.  Brown.  This  airplane  had  a 
wing  spread  of  67  feet  and  a  length  of  42  feet  8  inches 


MECHANICAL  EQUIVALENT  OF  HEAT          153 


183.  Joule's  experiment  on  the  heat  developed  by  friction. 

Joule  argued  that  if  the  heat  produced  by  friction  etc.  is 
indeed  merely  mechanical  energy  which  has  been  transferred 
to  the  molecules  of  the  heated  body,  then  the  same  number 
of  calories  must  always  be  produced  by  the  disappearance  of 
a  given  amount  of  mechanical  energy.  And  this  must  be 
true,  no  matter  whether  the  work  is  expended  in  overcoming 
the  friction  of  wood  011  wood,  of  iron  on  iron,  in  percussion, 
in  compression,  or  in  any  other  conceivable  way.  To  see 
whether  or  not  this  was  so  he  caused  mechanical  energy 
to  disappear  in  as  many  ways  as  possible  and  measured  in 
every  case  the  amount  of  heat  developed. 

In  his  first  experiment  he  caused  paddle  wheels  to  rotate  in  a  vessel 
of  water  by  means  of  falling  weights  W  (Fig.  168).  The  amount  of 
work  done  by  gravity  upon  the  weights  in  causing  them  to  descend 
through  any  distance  d  was  equal 
to  their  weight  W  times  this  dis- 
tance. If  the  weights  descended 
slowly  and  uniformly,  this  work 
was  all  expended  in  overcoming 
the  resistance  of  the  water  to 
the  motion  of  the  paddle  wheels 
through  it ;  that  is,  it  was  wasted 
in  eddy  currents  in  the  water. 
Joule  measured  the  rise  in  the 
temperature  of  the  water  and 
found  that  the  mean  of  his  three  FlG.  168>  Jouie>s  first  experiment  on 
best  trials  gave  427  gram  meters  the  mechanical  equivalent  of  heat 
as  the  amount  of  work  required 

to  develop  enough  heat  to  raise  a  gram  of  water  one  degree.  This  value, 
confirmed  by  modern  experiments,  is  now  generally  accepted  as  correct. 
He  then  repeated  the  experiment,  substituting  mercury  for  water,  and 
obtained  425  gram  meters  as  the  work  necessary  to  produce  a  calorie  of 
heat.  The  difference  between  these  numbers  is  less  than  was  to  have 
been  expected  from  the  unavoidable  errors  in  the  observations.  He 
then  devised  an  arrangement  in  which  the  heat  was  developed  by  the 
friction  of  iron  on  iron,  and  again  obtained  425. 


154  WORK  AND  HEAT  ENERGY 

x/ 

184.  Heat   produced   by   collision.     A   Frenchman    named 
Hirn  was  the  first  to  make  a  careful  determination  of  the 
relation  between  the  heat  developed  by  collision  and  the  kinetic 
energy  which  disappears.    He  allowed  a  steel  cylinder  to  fall 
through  a  known  height  and  crush  a  lead  ball  by  its  impact 
upon  it.    The  amount  of  heat  developed  in  the  lead  was  meas- 
ured by  observing  the  rise  in  temperature  of  a  small  amount  of 
water  into  which  the  lead  was  quickly  plunged.    As  the  mean 
of  a  large  number  of  trials  he  also  found  that  425  gram  meters 
of  energy  disappeared  for  each  calorie  of  heat  that  appeared. 

185.  Heat  produced  by  the  compression  of  a  gas.  Another  way 
in  which  Joule  measured  the  relation  between  heat  and  work 
was  by  compressing  a  gas  and  comparing  the  amount  of  work 
done  in  the  compression  with  the  amount  of  heat  developed. 

Every  bicyclist  is  aware  of  the  fact  that  when  he  inflates  his 
tires  the  pump  grows  hot.  This  is  due  partly  to  the  friction  of 
the  piston  against  the  walls,  but  chiefly  to  the  fact  that  the 
downward  motion  of  the  piston  is  transferred  to  the  molecules 
which  come  in  contact  with  it,  so  that  the  velocity  of  these 
molecules  is  increased.  The  principle  is  precisely  the  same 
as  that  involved  in  the  velocity  communicated  to  a  ball  by  a 
bat.  If  the  bat  is  held  rigidly  fixed  and  a  ball  thrown  against 
it,  the  ball  rebounds  with  a  certain  velocity ;  but  if  the  bat 
is  moving  rapidly  forward  to  meet  the  ball,  the  latter  rebounds 
with  a  much  greater  velocity.  So  the  molecules  which  in  their 
natural  motions  collide  with  an  advancing  piston  rebound 
with  greater  velocity  than  they  would  if  they  had  impinged 
upon  a  fixed  wall.  This  increase  in  the  molecular  velocity 
of  a  gas  on  compression  is  so  great  that  when  a  mass  of  gas 
at  0°  C.  is  compressed  to  one  half  its  volume,  the  temperature 
rises  to  87°  C. 

The  effect  may  be  strikingly  illustrated  by  the  fire  syringe  (Fig.  169). 
Let  a  few  drops  of  carbon  bisulphide  be  placed  on  a  small  bit  of  cotton, 
dropped  to  the  bottom  of  the  tube  A,  and  then  removed;  then  let  the 


MECHANICAL  EQUIVALENT  OF  HEAT          155 


FIG.  169.   The 
fire  syringe 


piston  B  be  inserted  and  very  suddenly  depressed.  Sufficient  heat  will 
be  developed  to  ignite  the  vapor,  and  a  flash  will  result.  (If  the  flash 
does  not  result  from  the  first  stroke,  withdraw  the  piston 
completely,  then  reinsert,  and  compress  again.) 

To  measure  the  heat  of  compression  Joule 
surrounded  a  small  compression  purnp  with 
water,  took  300  strokes  on  the  pump,  and  meas- 
ured the  rise  in  temperature  of  the  water.  As 
the  result  of  these  measurements  he  obtained 
444  gram  meters  as  the  mechanical  equivalent 
of  the  calorie.  The  experiment,  however,  could 
not  be  performed  with  great  exactness. 

Joule  also  measured  the  converse  effect, 
namely,  the  cooling  produced  in  a  gas  which 
is  pushing  forward  a  piston  and  thus  doing  work. 
He  obtained  437  grain  meters. 

186.  Significance  of  Joule's  experiments.    Joule  made  three 
other  determinations  of  the  relation  between  heat  and  work 
by  methods  involving  electrical  measurements.    He  published 
as  the  mean  of  all  his  determinations  426.4  gram  meters  as 
the  mechanical  equivalent  of  the  calorie.    But  the  value  of 
his  experiments  does  not  lie  primarily  in  the  accuracy  of  the 
final  results,  but  rather  in  the  proof  which  they  for  the  first 
time  furnished  that  whenever  a  given  amount  of  work  is  tvasted, 
no  matter  in  what  particular  way  this  waste  occurs,  the  same 
definite  amount  of  heat  always  appears. 

The  most  accurate  determination  of  the  mechanical  equiva- 
lent of  heat  was  made  by  Rowland  (see  opposite  p.  358)  (1848- 
1901)  in  1880.  He  obtained  427  gram  meters  (4.19  x  107  ergs). 
We  shall  generally  take  it  as  42,000,000  ergs.  The  mechan- 
ical equivalent  of  1  B.  T.  U.  is  778  foot  pounds. 

187.  The  conservation  of  energy.    We  are  now  in  a  position 
to  state  the  law  of  all  machines  in  its  most  general  form,  that 
is,  in  such  a  way  as  to  include  even  the  cases  where  friction 


156  WORK  AND  HEAT  ENERGY 

is  present.  It  is :  The  work  done  by  the  acting  force  is  equal  to 
the  sum  of  the  kinetic  and  potential  energies  stored  up  plus  the 
mechanical  equivalent  of  the  heat  developed. 

In  other  words,  whenever  energy  is  expended  on  a  machine  or 
device  of  any  kind,  an  exactly  equal  amount  of  energy  always 
appears  either  as  useful  work  or  as  heat.  The  useful  work  may 
be  represented  in  the  potential  energy  of  a  lifted  mass,  as 
when  water  is  pumped  up  to  a  reservoir;  or  in  the  kinetic 
energy  of  a  moving  mass,  as  when  a  stone  is  thrown  from  a 
sling;  or  in  the  potential  energies  of  molecules  whose  posi- 
tions with  reference  to  one  another  have  been  changed,  as 
when  a  spring  has  been  bent;  or  in  the  molecular  potential 
energy  of  chemically  separated  atoms,  as  when  an  electric 
current  separates  a  compound  substance.  The  ivasted  work 
always  appears  in  the  form  of  increased  molecular  motion, 
that  is,  in  the  form  of  heat.  This  important  generalization 
has  received  the  name  of  the  Principle  of  the  Conservation  of 
Energy.  It  may  be  stated  thus:  Energy  may  be  transformed, 
but  it  can  never  be  created  or  destroyed. 

188.  Perpetual  motion.  In  all  ages  there  have  been  men 
who  have  spent  their  lives  in  trying  to  invent  a  machine  out 
of  which  work  could  be  continually  obtained,  without  the  ex- 
penditure of  an  equivalent  amount  of  work  upon  it.  Such 
devices  are  called  perpetual-motion  machines.  The  possibility 
of  the  existence  of  such  a  device  is  absolutely  denied  by  the 
statement  of  the  principle  of  the  conservation  of  energy.  For 
only  in  case  there  is  no  heat  developed,  that  is,  in  case  there 
are  no  frictional  losses,  can  the  wrork  taken  out  be  equal  to 
the  work  put  in,  and  in  no  case  can  it  be  greater.  Since,  in 
fact,  there  are  always  some  frictional  losses,  the  principle  of  the 
conservation  of  energy  asserts  that  it  is  impossible  to  make  a 
machine  which  will  keep  itself  running  forever,  even  though  it 
does  no  useful  work ;  for  no  matter  how  much  kinetic  or  poten- 
tial energy  is  imparted  to  the  machine  to  begin  with,  there 


MECHANICAL  EQUIVALENT  OF  HEAT          157 

must  always  be  a  continual  drain  upon  this  energy  to  overcome 
frictional  resistances,  so  that  as  soon  as  the  wasted  work  has 
become  equal  to  the  initial  energy,  the  machine  must  stop. 

The  principle  of  the  conservation  of  energy  has  now 
gained  universal  recognition  and  has  taken  its  place  as  the 
corner  stone  of  all  physical  science. 

189.  Transformations  of  energy  in  a  power  plant.  The  transforma- 
tions of  energy  which  take  place  in  any  power  plant,  such  as  that  at 
Niagara,  are  as  follows :  The  energy  first  exists  as  the  potential  energy 
of  the  water  at  the  top  of  the  falls.  This  is  transformed  in  the  turbine 
pits  into  the  kinetic  energy  of  the  rotating  wheels.  These  turbines 
drive  dynamos  in  which  there  is  a  transformation  into  the  energy  of 
electric  currents.  These  currents  travel  on  wires  as  far  as  Syracuse, 
150  miles  away,  where  they  run  street  cars  and  other  forms  of  motors. 
The  principle  of  conservation  of  energy  asserts  that  the  work  which 
gravity  did  upon  the  water  in  causing  it  to  descend  from  the  top  to  the 
bottom  of  the  turbine  pits  is  exactly  equal  to  the  work  done  by  all  the 
motors,  plus  the  heat  developed  in  all  the  wires  and  bearings  and  in 
the  eddy  currents  in  the  water. 

Let  us  next  consider  where  the  water  at  the  top  of  the  falls  obtained 
its  potential  energy.  Water  is  being  continually  evaporated  at  the  sur- 
face of  the  ocean  by  the  sun's  heat.  This  heat  imparts  sufficient  kinetic 
energy  to  the  molecules  to  enable  them  to  break  away  from  the  attrac- 
tions of  their  fellows  and  to  rise  above  the  surface  in  the  form  of  vapor- 
The  lifted  vapor  is  carried  by  winds  over  the  continents  and  precipitated 
in  the  form  of  rain  or  snow.  Thus  the  potential  energy  of  the  water 
above  the  falls  at  Niagara  is  simply  transformed  heat  energy  of  the 
sun.  If  in  this  way  we  analyze  any  available  source  of  energy  at  man's 
disposal,  we  find  in  almost  every  case  that  it  is  directly  traceable 
to  the  sun's  heat  as  its  source.  Thus,  the  energy  contained  in  coal  is 
simply  the  energy  of  separation  of  the  oxygen  and  carbon  which  were 
separated  in  the  processes  of  growth.  This  separation  was  effected  by 
the  sun's  rays. 

The  earth  is  continually  receiving  energy  from  the  sun  at  the  rate  of 
342,000,000,000,000  horse  power,  or  about  a  quarter  of  a  million  horse 
power  per  inhabitant.  We  can  form  some  conception  of  the  enormous 
amount  of  energy  that  the  sun  radiates  in  the  form  of  heat  by  reflecting 
that  the  amount  received  by  the  earth  is  not  more  than 


,0  0  0,0  0  • 


158  WORK  AND  HEAT  ENERGY 

of  the  total  given  out.  Of  the  amount  received  by  the  earth  not  more 
than  1  01OQ  part  is  stored  up  in  animal  and  vegetable  life  and  lifted  water. 
This  is  practically  all  of  the  energy  which  is  available  on  the  earth  for 
man's  use. 

QUESTIONS  AND  PROBLEMS 

1.  Show  that  the  energy  of  a  waterfall  is  merely  transformed  solar 
energy. 

2.  Analyze  the  transformations  of  energy  which  occur  when  a  bullet 
is  fired  vertically  upward. 

3.  Meteorites  are  small,  cold  bodies  moving  about  in  space.  Why  do 
they  become  luminous  when  they  enter  the  earth's  atmosphere  ? 

4.  The  Niagara  Falls  are  1GO  ft.  high.    How  much  warmer  is  the 
water  at  the  bottom  of  the  falls  than  at  the  top? 

5.  How  many  B.  T.  U.  are  required  to  warm  10  Ib.  of  water  from 
freezing  to  boiling  ? 

6.  Two  and  a  half  gallons  of  water  (  =  20  Ib.)  were  warmed  from, 
68°F.  to  212°F.  If  the  heat  energy  put  into  the  water  could  all  have  beei* 
made  to  do  useful  work,  how  high  could  10  tons  of  coal  have  been 
hoisted  ? 

SPECIFIC  HEAT 

190.  Definition  of  specific  heat.  When  we  experiment  upon 
different  substances,  we  find  that  it  requires  wholly  different 
amounts  of  heat  energy  to  produce  in  one  gram  of  mass  one 
degree  of  change  in  temperature. 

Let  100  g.  of  lead  shot  be  placed  in  one  test  tube,  100  g.  of  bits  of 
iron  wire  in  another,  and  100  g.  of  aluminium  wire  in  a  third.  Let 
them  all  be  placed  in  a  pail  of  boiling  water  for  ten  or  fifteen  minutes, 
care  being  taken  not  to  allow  any  of  the  water  to  enter  any  of  the  tubes. 
Let  three  small  vessels  be  provided,  each  Of  which  contains  100  g.  oi: 
water  at  the  temperature  of  the  room.  Let  the  heated  shot  be  poured 
into  the  first  beaker,  and  after  thorough  stirring  let  the  rise  in  the 
temperature  of  the  water  be  noted.  Let  the  same  be  done  with  the 
other  metals.  The  aluminium  will  be  found  to  raise  the  temperature 
about  twice  as  much  as  the  iron,  and  the  iron  about  three  times  as 
much  as  the  lead.  Hence,  since  the  three  metals  have  cooled  through 
approximately  the  same  number  of  degrees,  we  must  conclude  that 
about  six  times  as  much  heat  has  passed  out  of  the  aluminium  as  out 
of  the  lead;  that  is;  each'  gram  of  aluminium  in  cooling  1°C.  gives  out 
about  six  times  as  many  calories  as  a  gram  of  lead. 


SPECIFIC  HEAT  159 

The  number  of  calories  taken  up  by  1  gram  of  a  substance 
when  its  temperature  rises  through  1°  (7.,  or  given  up  when  it 
falls  through  1°  (7.,  is  called  the  specific  heat  of  that  substance. 

It  will  be  seen  from  this  definition,  and  the  definition  of 
the  calorie,  that  the  specific  heat  of  water  is  1. 

191.  Determination  of  specific  heat  by  the  method  of  mix- 
tures. The  preceding  experiments  illustrate  a  method  for 
measuring  accurately  the  specific  heats  of  different  substances  ; 
for,  in  accordance  with  the  principle  of  the  conservation  of 
energy,  when  hot  and  cold  bodies  are  mixed,  as  in  these  ex- 
periments, so  that  heat  energy  passes  from  one  to  the  other, 
the  gain  in  the  heat  energy  of  one  must  be  just  equal  to  the  loss 
in  the  heat  energy  of  the  other. 

This  method  is  by  far  the  most  common  one  for  determin- 
ing the  specific  heats  of  substances.  It  is  known  as  the  method 
of  mixtures. 

Suppose,  to  take  an  actual  case,  that  the  initial  temperature  of  the 
shot  used  in  §  190  was  95°  C.  and  that  of  the  water  19.7°,  and  that,  after 
mixing,  the  temperature  of  the  water  and  shot  was  22°.  Then,  since 
100  g.  of  water  has  had  its  temperature  raised  through  22°  —  19.7°  =  2.3°, 
we  know  that  230  calories  of  heat  have  entered  the  water.  Since  the 
temperature  of  the  shot  fell  through  95°  —  22°  =  73°,  the  number  of 
calories  given  up  by  the  100  g.  of  shot  in  falling  1°  was  ^f-  =  3.15. 
Hence  the  specific  heat  of  lead,  that  is,  the  number  of  calories  of  heat  given 

Q     -|   £T 

up  by  1  gram  of  lead  when  its  temperature  falls  1°C.,  is  — - —  =  .0315. 

Or,  again,  we  may  work  out  the  problem  algebraically  as  follows : 
Let  x  equal  the  specific  heat  of  lead.  Then  the  number  of  calories  which 
come  out  of  the  shot  is  its  mass  times  its  specific  heat  times  its  change  in 
temperature,ihat  is,  100  X  a:  x  (95  —  22) ;  and,  similarly,  the  number  which 
enter  the  water  is  the  same,  namely,  100  x  1  x  (22  —  19.7).  Hence  we  have 

100  (95  -  22)  x  =  100  (22  -  19.7),     or     x  =  .0315. 

By  experiments  of  this  sort  the  specific  heats  of  some  of 
the  common  substances  have  been  found  to  be  as  follows: 


160  WOEK  AND  HEAT  ENEKGY 

TABLE  OF  SPECIFIC  HEATS 

Aluminium 218  Iron 113 

Brass 094  Lead 0315 

Copper 095  Mercury 0333 

Glass 2  Platinum 032 

Gold 0316  Silver 0568 

Ice    .  .504  Zinc  .0935 


QUESTIONS  AND  PROBLEMS 

1.  A  barrelful  of  tepid  water,  when  poured  into  a  snowdrift,  melts 
much  more  snow  than  a  cupful  of  boiling  water  does.    Which  has  the 
greater  quantity  of  heat  ? 

2.  Why  is  a  liter  of  hot  water  a  better  foot  warmer  than  an  equal 
volume  of  any  substance  in  the  preceding  table  ? 

3.  The  specific  heat  of  water  is  much  greater  than  that  of  any  other 
liquid  or  of  any  solid.    Explain  how  this  accounts  for  the  fact  that  an 
island  in  mid-ocean  undergoes  less  extremes  of  temperature  than  an 
inland  region. 

4.  How  many  calories  are  required  to  heat  a  laundry  iron  weighing 
3  kg.  from  20°  C.  to  130°  C.? 

5.  How  many  B.  T.  U.  are  required  to  warm  a  6-pound  laundry 
iron  from  75°  F.  to  250°  F.  ? 

6.  If  100  g.  of  mercury  at  95°  C.  are  mixed  with  100  g.  of  water  at 
15°  C.,  and  if  the  resulting  temperature  is  17.6°  C.,  what  is  the  specific 
heat  of  mercury? 

•7.  Tf  200  g.  of  water  at  80°  C.  are  mixed  with  100  g.  of  water  at 
10° C.,  what  will  be  the  temperature  of  the  mixture?  (Let  x  equal  the 
final  temperature ;  then  100  (x  — 10)  calories  are  gained  by  the  cold 
water,  while  200  (80  —  a:)  calories  are  lost  by  the  hot  water.) 

8.  What  temperature  will  result  if  400  g.  of  aluminium  at  100°  C. 
are  placed  in  500  g.  of  water  at  20°  C.  ? 

9.  Eight  pounds  of  water  were  placed  in  a  copper  kettle  weighing 
2.5  Ib.    How  many  B.  T.  U.  are  required  to  heat  the  water  and  the  kettle 
from  70° F.  to  212° F.?   If  4.3  cu.  ft.  of  gas  was  used  to  do  this,  and  if 
each  cubic  foot  of  gas  on  being  burned  yields  625  B.  T.  U.,  what  is  the 
efficiency  of  the  heating  apparatus? 

10.  If  a  solid  steel  projectile  were  shot  with  a  velocity  of  1000  m. 
(3048  ft.)  per  second  against  an  impenetrable  steel  target,  and  all  the  heat 
generated  were  to  go  toward  raising  the  temperature  of  the  projectile, 
what  would  be  the  amount  of  the  increase  ? 


CHAPTER  X 

CHANGE  OF  STATE 

FUSION  * 

192.  Heat  Of  fusion.  If  on  a  cold  day  in  winter  a  quantity  of  snow 
is  brought  in  from  out  of  doors,  where  the  temperature  is  below  0°C. 
and  placed  over  a  source  of  heat,  a  thermometer  plunged  into  the  snow 
will  be  found  to  rise  slowly  until  the  temperature  reaches  0°C.,  when 
it  will  become  stationary  and  remain  so  during  all  the  time  the  snow 
is  melting,  provided  only  that  the  contents  of  the  vessel  are  continu- 
ously and  vigorously  stirred.  As  soon  as  the  snow  is  all  melted,  the 
temperature  will  begin  to  rise  again. 

Since  the  temperature  of  ice  at  0°  C.  is  the  same  as  the 
temperature  of  water  at  0°  C.,  it  is  evident  from  this  experiment 
that  when  ice  is  being  changed  to  water,  the  entrance  of  heat 
energy  into  it  does  not  produce  any  change  in  the  average 
kinetic  energy  of  its  molecules.  This  energy  must  therefore 
all  be  expended  in  pulling  apart  the  molecules  of  the  crystals 
of  which  the  ice  is  composed,  and  thus  reducing  it  to  a  form 
in  which  the  molecules  are  held  together  less  intimately,  that 
is,  to  the  liquid  form.  In  other  words,  the  energy  which  existed 
in  the  flame  as  the  kinetic  energy  of  molecular  motion  has 
been  transformed,  upon  passage  into  the  melting  solid,  into 
the  potential  energy  of  molecules  which  have  been  pulled 
apart  against  the  force  of  their  mutual  attraction.  The  number 

*This  subject  should  be  preceded  by  a  laboratory  exercise  on  the  curve 
of  cooling  through  the  point  of  fusion,  and  followed  by  a  determination  of 
the  heat  of  fusion  of-  ice.  See,  for  example,  Experiments  21  and  22  of  the 
authors1  Manual. 

161 


162  CHANGE  OF  STATE 

of  calories  of  heat  energy  required  to  melt  one  gram  of  any 
substance  without  producing  any  change  in  its  temperature  is 
called  the  heat  of  fusion  of  that  substance. 

193.  Numerical  value  of  heat  of  fusion  of  ice.    Since  it  is 
found  to  require  about  80  times  as  long  for  a  given  flame  to 
melt  a  quantity  of  snow  as  to  raise  the  melted  snow  through 
1°  C.,  we  conclude  that  it  requires  about  80  calories  of  heat 
to  melt  1  g.  of  snow  or  ice.    This  constant  is,  however,  much 
more  accurately  determined  by  the  method  of  mixtures.    Thus, 
suppose  that  a  piece  of  ice  weighing  131  g.  is  dropped  into 
500  g.  of  water  at  40°  C.,  and  suppose  that  after  the  ice  is  all 
melted  the  temperature  of  the  mixture  is  found  to  bo  15°  C. 
The  number  of  calories  which  have  come  out  of  the  water  is 
500  x  (40  -  15)  =  12,500.    But  131  x  15  =  1965  calories  of 
this  heat  must  have  been  used  in  raising  the  ice  from  0°  C. 
to  15°  C.  after  the  ice,  by  melting,  became  water  at  0°.    The 
remainder  of  the  heat,  namely,  12,500  —  1965  =  10,535,  must 
have  been  used  in  melting  the  131  g.  of  ice.     Hence  the 
number  of  calories  required  to  melt  1  g.  of  ice  is  1 "  j»  \  5  =  80.4. 

To  state  the  problem  algebraically,  let  x  =  the  heat  of  fusion 
of  ice.    Then  we  have 

131  x  +  1965  -  12,500  ;  that  is,  x  =  80.4. 

According  to  the  most  careful  determinations  the  heat  of  fusion 
of  ice  is  80.0  calories. 

194.  Energy  transformation   in  fusion.    The   heat  energy 
that  goes  into  a  body  to  change  it  from  the  solid  state  to  the 
liquid  state  no  longer  exists  as  heat  within  the  liquid.    It  has 
ceased  to  exist  as  heat  energy  at  all,  having  been  transformed 
into  molecular  potential  energy ;  that  is,  the  heat  which  disap- 
pears represents  the  work  that  was  done  in  effecting  the  change 
of  state )   and   it   is,   therefore,   the   exact   equivalent   of   the 
potential  energy  gained  by  the  rearranged  molecules.    This  is 
strictly  in  accord  with  the  law  of  conservation  of  energy. 


FUSION 


163 


195.  Heat  given  out  when  water  freezes.    Let  snow  and  salt  be 
added  to  a  beaker  of  water  until  the  temperature  of  the  liquid  mixture 
is  as  low  as  —  10°  C.  or  —  12°  C.    Then  let  a  test  tube  containing  a  ther- 
mometer and  a  quantity  of  pure  water  be  thrust  into  the  cold  solution. 
If  the  thermometer  is  kept  very  quiet,  the  temperature  of  the  water  in  the 
test  tube  will  fall  four  or  five  or  even  ten  degrees  below  0°  C.  without 
producing  solidification.   But  as  soon  as  the  thermometer  is  stirred,  or  a 
small  crystal  of  ice  is  dropped  into  the  neck  of  the  tube,  the  ice  crystals 
will  form  with  great  suddenness,  and  at  the  same  time  the  thermometer 
will  rise  to  0°  C.,  where  it  will  remain  until  all  the  water  is  frozen. 

The  experiment  shows  in  a  very  striking  way  that  the  proc- 
ess of  freezing  is  a  heat-evolving  process.  This  was  to  have 
been  expected  from  the  principle  of  the  conservation  of  energy ; 
for  since  it  takes  80  calories  of  heat  energy  to  turn  a  gram  of  ice 
at  0°  C.  into  water  at  0°  (7.,  this  amount  of  energy  must  reappear 
when  the  water  turns  back  to  ice. 

196.  Use  made  of  energy  transformations  in  melting  and 
freezing.    A  refrigerator  (Fig.  170)  is  a  box  constructed  with 
double  walls  so  as  to  make  it  difficult  for  heat  to  pass  in  from 
the  outside.   Ice  is  kept  in  the  upper 

part  of  one  compartment  so  as  to  cool 
the  air  at  the  top,  which,  because  of 
its  greater  density  when  cool,  settles 
and  causes  a  circulation  as  indicated 
by  the  arrows.  To  melt  each  gram  of 
ice  80  calories  must  be  taken  from 
the  air  and  food  within  the  refrigera- 
tor. If  the  ice  did  not  melt,  it  would 
be  worthless  for  use  in  refrigerators. 
The  heat  given  off  by  the  freezing 
of  water  is  often  turned  to  practical 
account ;  for  example,  tubs  of  water  are  sometimes  placed  in 
vegetable  cellars  to  prevent  the  vegetables  from  freezing. 
The  effectiveness  of  this  procedure  is  due  to  the  fact  that 
the  temperature  at  which  the  vegetables  freeze  is  slightly 


FIG.  170.   A  refrigerator 


164  CHANGE   OF  STATE 

lower  than  0°  C.  As  the  temperature  of  the  cellar  falls  the 
water  therefore  begins  to  freeze  first,  and  in  so  doing  evolves 
enough  heat  to  prevent  the  temperature  of  the  room  from 
falling  as  far  below  0°  C.  as  it  otherwise  would. 

It  is  partly  because  of  the  heat  evolved  by  the  freezing  of 
large  bodies  of  water  that  the  temperature  never  falls  so  low 
in  the  vicinity  of  large  lakes  as  it  does  in  inland  localities. 
,  197.  Melting  points  of  crystalline  substances.  If  a  piece  of 
ice  is  placed  in  a  vessel  of  boiling  water  for  an  instant  and 
then  removed  and  wiped,  it  will  not  be  found  to  be  in  the 
slightest  degree  warmer  than  a  piece  of  ice  which  has  not  been 
exposed  to  the  heat  of  the  warm  water.  The  melting  point  of 
ice  is  therefore  a  perfectly  fixed,  definite  temperature,  above 
which  the  ice  can  never  be  raised  so  long  as  it  remains  ice, 
no  matter  how  fast  heat  is  applied  to  it.  All  crystalline  sub- 
stances are  found  to  behave  exactly  like  ice  in  this  respect, 
each  substance  of  this  class  having  its  characteristic  melting 
point.  The  following  table  gives  the  melting  points  of  some 
of  the  commoner  crystalline  substances : 


Mercury  . 
Ice  . 
Benzine    . 

-39°C. 
0°C. 

7°C. 

Sulphur  .  . 
Tin  .  .  . 
Lead  . 

114°  C. 
233°C. 
330°C. 

Silver  .     . 
Copper 
Cast  iron  . 

.  954°C. 
.  1100°C. 
.  1200°  C. 

Acetic  acid   . 

17°C. 

Zinc  .  .  . 

433°C. 

Platinum  . 

.  1775°C. 

Paraffin    .     . 

54°C. 

Aluminium  . 

650°C. 

Iridium     . 

.  1950°C. 

We  may  summarize  the  experiments  upon  melting  points  of 
crystalline  substances  in  the  two  following  laws : 

1.  The  temperatures  of  solidification  and  fusion  are  the  same. 

2.  The  temperature  of  the  melting  or  solidifying  substance 
remains  constant  from  the  moment  at  which  melting  or  solidi- 
fication begins  until  the  process  is  completed. 

198.  Fusion  of  noncrystalline,  or  amorphous,  substances.  Let 
the  end  of  a  glass  rod  be  held  in  a  Bunsen  flame.  Instead  of  changing 
suddenly  from  the  solid  to  the  liquid  state,  it  will  gradually  grow  softer 


FUSION  165 

and  softer  until,  if  the  rod  is  not  too  thick  and  the  flame  is  sufficiently 
hot,  a  drop  of  molten  glass  will  finally  fall  from  the  end  of  the  rod. 

If  the  temperature  of  the  rod  had  been  measured  during 
this  process,  it  would  have  been  found  to  be  continually  rising. 
This  behavior,  so  completely  unlike  that  of  crystalline  sub- 
stances, is  characteristic  of  tar,  wax,  resin,  glue,  gutta-percha, 
alcohol,  carbon,  and  in  general  of  all  amorphous  substances. 
Such  substances  cannot  be  said  to  have  any  definite  melting 
points  at  all,  for  they  pass  through  all  stages  of  viscosity  both 
in  melting  and  in  solidifying.  It  is  in  virtue  of  this  property 
that  glass  and  other  similar  substances  can  be  heated  to  soft- 
ness and  then  molded  or  rolled  into  any  desired  shape. 

199.  Change  of  volume  on  solidifying.  One  has  only  to 
reflect  that  ice  floats,  or  that  bottles  or  crocks  of  water  burst 
when  they  freeze,  in  order  to  know  that  water  expands  upon 
solidifying.  In  fact,  1  cubic  foot  of  water  becomes  1.09  cubic 
feet  of  ice,  thus  expanding  more  than  one  twelfth  of  its  initial 
volume  when  it  freezes.  This  may  seem  strange  in  view  of 
the  fact  that  the  molecules  are  certainly  more  closely  knit 
together  in  the  solid  than  in  the  liquid  state ;  but  the  strange- 
ness disappears  when  we  reflect  that  the  molecules  of  water  in 
freezing  group  themselves  into  crystals,  and  that  this  operation 
presumably  leaves  comparatively  large  free  spaces  between 
different  crystals,  so  that,  although  groups  of  individual  mole- 
cules are  more  closely  joined  than  before,  the  total  volume 
occupied  by  the  whole  assemblage  of  molecules  is  greater. 

But  the  great  majority  of  crystalline  substances  contract 
upon  solidifying  and  expand  upon  liquefying.  Water,  anti- 
mony, bismuth,  cast  iron,  and  a  few  alloys  containing  antimony 
or  bismuth  are  the  chief  exceptions.  It  is  only  from  substances 
which  expand,  or  which  change  in  volume  very  little  on  solidi- 
fying, that  sharp  castings  can  be  made ;  for  it  is  clear  that 
contracting  substances  cannot  retain  the  shape  of  the  mold. 
It  is  for  this  reason  that  gold  and  silver  coins  must  be  stamped 


166  CHANGE  OF  STATE 

rather  than  cast.  Any  metal  from  which  type  is  to  be  cast 
must  be  one  which  expands  upon  solidifying,  for  it  need 
scarcely  be  said  that  perfectly  sharp  outlines  are  indispensable 
to  good  type.  Ordinary  type  metal  is  an  alloy  of  lead,  anti- 
mony, and  copper,  which  fulfills  these  requirements. 

200.  Effect   of   the   expansion  which  water   undergoes   on 
freezing.    If  water  were  not  unlike  most  substances  in  that  it 
expands  on  freezing,  many,  if  not  all,  of  the  forms  of  life  which 
now  exist  on  the  earth  would  be  impossible ;  for  in  winter 
the  ice  would  sink  in  ponds  and  lakes  as  fast  as  it  froze,  and 
soon  our  rivers,  lakes,  and  perhaps  our  oceans  also  would 
become  solid  ice. 

The  force  exerted  by  the  expansion  of  freezing  water  is  very 
great.  Steel  bombs  have  been  burst  by  filling  them  with  water 
and  exposing  them  on  cold  winter  nights.  One  of  the  chief 
agents  in  the  disintegration  of  rocks  is  the  freezing  and  conse- 
quent expansion  of  water  which  has  percolated  into  them. 

201.  Pressure  lowers  the  melting  point  of  substances  which 
expand  on  solidifying.    Since  the  outside  pressure  acting  on 
the  surface  of  a  body  tends  to  prevent  its  expansion,  we  should 
expect  that  any  increase  in  the  outside  pressure  would  tend 
to  prevent  the  solidification  of  substances  which  expand  upon 
freezing.    It  ought  therefore  to  require  a  lower  temperature 
to  freeze  ice  under  a  pressure  of  two  atmospheres  than  under 
a  pressure   of  one.    Careful   experiments  have  verified  this 
conclusion  and  have  shown  that  the  melting  point  of  ice  is 
lowered  .0075°  C.  for  an  increase  of  one  atmosphere  in  the 
outside  pressure.   Although  this  lowering  is  so  small  a  quantity, 
its  existence  may  be  shown  as  follows : 

Let  two  pieces  of  ice  be  pressed  firmly  together  beneath  the  surface 
of  a  vessel  full  of  warm  water.  When  taken  out  they  will  be  found  to 
be  frozen  together,  in  spite  of  the  fact  that  they  have  been  immersed 
in  a  medium  much  warmer  than  the  freezing  point  of  water.  The 
explanation  is  as  follows  : 


FUSION  167 

At  the  points  of  contact  the  pressure  reduces  the  freezing  point  of 
the  ice  below  0°  C.,  and  hence  it  rnelts  and  gives  rise  to  a  thin  film  of 
water  the  temperature  of  which  is  slightly  below  0°  C.  When  this 
pressure  is  released,  the  film  of  water  at  once  freezes,  for  its  tempera- 
ture is  below  the  freezing  point  corresponding  to  ordinary  atmospheric 
pressure.  The  same  phenomenon  may  be  even  more  strikingly  illus- 
trated by  the  following  experiment : 

Let  two  weights  of  from  5  to  10  kg.  be  hung  by  a  wire  over  a  block 
of  ice  as  in  Fig.  171.  In  half  an  hour  or  less  the  wire  will  be  found  to 
have  cut  completely  through  the  block, 
leaving  the  ice,  however,  as  solid  as  at 
first.  The  explanation  is  as  follows : 
Just  below  the  wire  the  ice  melts  be- 
cause of  the  pressure  ;  as  the  wire  sinks 
through  the  layer  of  water  thus  formed, 
the  pressure  on  the  water  is  relieved 
and  it  immediately  freezes  again  above 
the  wire. 

Geologists  believe  that  the  con- 
tinuous flow  of   glaciers  is  partly  ElG>  171>  Regelation 
due  to  the  fact  that  the  ice  melts 

at  points  where  the  pressures  become  large,  and  freezes  again 
when  these  pressures  are  relieved.  This  process  of  melting 
under  pressure  and  freezing  again  as  soon  as  the  pressure  is 
relieved  is  known  as  regelation. 

Substances  ivhich  expand  on  solidifying  have  their  melting 
points  lowered  by  pressure,  and  those  which  contract  on  solidify- 
ing have  their  melting  points  raised  by  pressure. 

QUESTIONS  AND  PROBLEMS 

1.  What  is  the  meaning  of  the  statement  that  the  heat  of  fusion  of 
mercury  is  2.8  ? 

2.  Explain  how  the  presence  of  ice  keeps  the  interior  of  a  refrig- 
erator from  becoming  warm. 

3.  How  many  times  as  much  heat  is  required  to  melt  any  piece  of 
ice  as  to  warm  the  resulting  water  1°  C.  ?    1°  F.  ?  How  many  B.  T.  U.  are 
required  to  melt  1  Ib.  of  ice?     How  many  foot  pounds  of  energy  are 
required  to  do  the  work  of  melting  1  Ib.  of  ice  ? 


168  CHANGE  OF  STATE 

4.  If  the  heat  of  fusion  of  ice  were  40  instead  of  80,  how  would  this 
affect  the  quantity  of  ice  that  would  have  to  be  bought  for  the  refriger- 
ator during  the  summer? 

5.  Five  pounds  of  ice  melted  in  1  hr.  in  an  unopened  refrigerator. 
How   many  B.  T.  U.  caine  through  the  walls  of  the   refrigerator  in 
the  hour? 

6.  Just  what  will  occur  if  1000  calories  be  applied  to  20  g.  of  ice  at 
0°C.? 

7.  How  many  grains  of  ice  must  be  put  into  200  g.  of  water  at  40°  C. 
to  lower  the  temperature  10°  C.  ? 

8.  How  many  grams  of  ice  must  be  put  into  500  g.  of  water  at  50°  C. 
to  lower  the  temperature  to  10°  C.? 

9.  Why  will   snow  pack  into  a  snowball  if  the  snow  is  melting, 
but  not  if  it  is  much  below  0°  C.  ? 


EVAPORATION  AND  THE  PROPERTIES  OF  VAPORS 

202.  Evaporation  and  temperature.    If  it  is  true  that  in- 
crease in  temperature  means  increase  in  the  mean  velocity 
of  molecular  motion,  then  the  number  of  molecules  which 
chance  in  a  given  time  to  acquire  the  velocity  necessary  to 
carry  them  into  the  space  above  the  liquid  ought  to  increase 
as  the  temperature  increases ;  that  is,  evaporation  ought  to 
take  place  more  rapidly  at  high  temperatures  than  at  low. 
Common  observation  teaches  that  this  is  true.    Damp  clothes 
become  dry  under  a  hot  flatiron  but  not  under  a  cold  one ; 
the  sidewalk  dries  more  readily  in  the  sun  than  in  the  shade ; 
we  put  wet  objects  near  a  hot  stove  or  radiator  when  we 
wish  them  to  dry  quickly. 

203.  Evaporation  of  solids, —  sublimation.    That  the  mole- 
cules of  a  solid  substance  are  found  in  a  vaporous  condition 
above  the  surface  of  the  solid,  as  well  as  above  that  of  a 
liquid,   is   proved   by  the   often-observed   fact  that  ice   and 
snow  evaporate  even  though  they  are  kept  constantly  below 
the  freezing   point.    Thus,  wet  clothes   dry  in  winter   after 
freezing.    An  even  better  proof  is  the  fact  that  the  odor  of 
camphor  can  be  detected  many  feet  away  from  the  camphor 


EVAPORATION  169 

crystals.    The  evaporation  of  solids  may  be  rendered  visible 
by  the  following  striking  experiment: 

Let  a  few  crystals  of  iodine  be  placed  on  a  watch  glass  and  heated 
gently  with  a  Bunsen  flame.  The  visible  vapor  of  iodine  will  appear 
above  the  crystals,  though  none  of  the  liquid  is  formed. 

A  great  many  substances  at  high  temperatures  pass  from 
the  solid  to  the  gaseous  condition  without  passing  through 
the  liquid  state.  The  vaporization  of  a  solid  is  called  sublimation. 

204.  Saturated  vapor.  If  a  liquid  is  placed  in  an  open  vessel, 
there  ought  to  be  no  limit  to  the  number  of  molecules  which 
can  be  lost  by  evaporation,  for  as  fast  as  the  molecules  emerge 
from  the  liquid  they  are  carried  away  by  air  currents.  As  a 
matter  of  fact,  experience  teaches  that  water  left  in  an  open 
dish  does  waste  away  until  the  dish  is  completely  dry. 

But  suppose  that  the  liquid  is  evaporating  into  a  closed 
space,  such  as  that  shown  in  Fig.  172.  Since  the  molecules 
which  leave  the  liquid  cannot  escape  from  the 
space  S,  it  is  clear  that  as  time  goes  on  the 
number  of  molecules  which  have  passed  off 
from  the  liquid  into  this  space  must  contin- 
ually increase ;  in  other  words,  the  density  of 
the  vapor  in  S  must  grow  greater  and  greater. 
But  there  is  an  absolutely  definite  limit  to 
the  density  which  the  vapor  can  attain ;  for 
as  soon  as  it  reaches  a  certain  value,  depending  on  the  tem- 
perature and  on  the  nature  of  the  liquid,  the  number  of 
molecules  returning  per  second  to  the  liquid  surface  will  be 
exactly  equal  to  the  number  escaping.  The  vapor  is  then 
said  to  be  saturated. 

If  the  density  of  the  vapor  is  lessened  temporarily  by  in- 
creasing the  size  of  the  vessel  S,  more  molecules  will  escape 
from  the  liquid  per  second  than  return  to  it,  until  the  density 
of  the  vapor  has  regained  its  original  value. 


170 


CHANGE  OF  STATE 


If,  on  the  other  hand,  the  density  of  the  vapor  has  been 
increased  by  compressing  it,  more  molecules  return  to  the 
liquid  per  second  than  escape,  and  the  density  of  the  vapor 
falls  quickly  to  its  saturated  value.  We  learn,  then,  that  the 
density  of  the  saturated  vapor  of  a  liquid  depends  on  the  tem- 
perature alone  and  cannot  be  affected  by  changes  in  volume. 

205.  Pressure  of  a  saturated  vapor.  Just  as  a  gas  exerts  a 
pressure  against  the  walls  of  the  containing  vessel  by  the 
blows  of  its  moving  molecules,  so  also  does  a  confined  vapor. 
But  at  any  given  temperature  the  density  of  a  saturated  vapor 
can  have  only  a  definite  value ;  that  is,  there  can  be  only  a 
definite  number  of  molecules  per  cubic  centimeter.  It  fol- 
lows, therefore,  that  just  as  at  any  temperature  the  saturated 
vapor  can  have  only  one  density,  so 
also  it  can  have  only  one  pressure. 
This  pressure  is  called  the  pressure 
of  the  saturated  vapor  correspond- 
ing to  the  given  temperature. 

Let  two  Torricelli  tubes  be  set  up  as 
in  Fig.  173,  and  with  the  aid  of  a  curved 
pipette  (Fig.  173)  let  a  drop  of  ether  be 
introduced  into  the  bottom  of  tube  1. 
This  drop  will  at  once  rise  to  the  top, 
and  a  portion  of  it  will  evaporate  into 
the  vacuum  which  exists  above  the  mer- 
cury. The  pressure  of  this  vapor  will 
push  down  the  mercury  column,  and  the 
number  of  centimeters  of  this  depres- 
sion will  of  course  be  a  measure  of  the 
pressure  of  the  vapor.  It  will  be  observed 
that  the  mercury  will  fall  almost  in- 
stantly to  the  lowest  level  which  it  will  ever  reach,  —  a  fact  which  indi- 
cates that  it  takes  but  a  very  short  time  for  the  condition  of  saturation 
to  be  attained. 

The  pressure  of  the  saturated  ether  vapor  at  the  temperature 
of  the  room  will  be  found  to  be  as  much  as  40  centimeters. 


FIG.  173.     Vapor   pressure  of 
a  saturated  vapor 


EVAPORATION 


1T1 


Let  a  Bunsen  flame  be  passed  quickly  across  the  tubes  of  Fig.  173^ 
near  the  upper  level  of  the  mercury.  The  vapor  pressure  will  increase 
rapidly  in  tube  1,  as  shown  by  the  fall  of  the  mercury  column. 

The  experiment  proves  that  both  the  pressure  and  the 
density  of  a  saturated  vapor  increase  rapidly  with  the  tem- 
perature. This  was  to  have  been  expected  from  our  theory, 
for  increasing  the  temperature  of  the  liquid  increases  the 
mean  velocity  of  its  molecules  and  hence  increases  the  num- 
ber which  attain  each  second  the  velocity  necessary  for  escape. 
How  rapidly  the  density  and  pressure  of  saturated  water 
vapor  increase  with  temperature  may  be  seen  from  the  fol- 
lowing table: 

TABLE  OF  CONSTANTS  OF  SATURATED  ABATER  VAPOR 

The  table  shows  the  pressure  P,  in  millimeters  of  mercury,  and  the 
density  D  of  aqueous  vapor  saturated  at  temperatures  t°  C. 


t. 

P. 

D. 

t. 

P. 

D. 

t. 

P. 

D. 

-  10° 

2.2 

.0000023 

4° 

6.1 

.0000064 

18° 

15.3 

.0000152 

-  9° 

2.3 

.0000025 

5° 

6.5 

.0000068 

19° 

16.3 

.0000162 

-  8° 

2.5 

.0000027 

6° 

7.0 

.0000073 

20° 

17.4 

.0000172 

-  7° 

2.7 

.0000029 

7° 

7.5 

.0000077 

21° 

18.5 

.0000182 

-  6° 

2.9 

.0000032 

8° 

8.0 

.0000082 

22° 

19.6 

.0000193 

-  5° 

3.2 

.0000034 

9° 

8.5 

.0000087 

23° 

20.9 

.0000204 

40 

3.4 

.0000037 

10° 

9.1 

.0000093 

24° 

22.2 

.0000216 

-  3° 

3.7 

,0000040 

11° 

9.8 

.0000100 

25° 

23.5 

.0000229 

-  2° 

3.9 

.0000042 

12° 

10.4 

.0000106 

26° 

25.0 

.0000242 

JO 

4.2 

.0000045 

13° 

11.1 

.0000112 

27° 

26.5 

.0000256 

0° 

4.6 

.0000049 

14° 

11.9 

.0000120 

28° 

28.1 

.0000270 

1° 

4.9 

.0000052 

15° 

12.7 

.0000128 

30° 

31.5 

.0000301 

2° 

5.3 

.0000056 

16° 

13.5 

.0000135 

35° 

41.8 

.0000393 

3° 

5.7 

.0000060 

17° 

14.4 

.0000144 

40° 

54.9 

.0000509 

206.  The  influence  of  air  on  evaporation.  We  observed  that 
when  ether  was  inserted  into  a  Torricelli  tube  the  mercury 
fell  very  suddenly  to  its  final  position,  showing  that  in  a 
vacuum  the  condition  of  saturation  is  reached  almost  instantly. 


172  CHANGE  OF  STATE 

This  was  to  have  been  expected  from  the  great  velocities 
which  we  found  the  molecules  of  gases  and  vapors  to  possess. 

Let  air  be  introduced  into  tube  2  (Fig.  173)  until  the  mercury  col- 
umn stands  at  a  height  of  from  45  to  55  cm.  Measure  the  height  of 
the  mercury  column.  In  order  to  see  what  effect  the  presence  of  air 
has  upon  evaporation,  let  a  drop  of  ether  be  introduced  into  the  tube. 
The  mercury  will  not  be  found  to  sink  instantly  to  its  final  level  as 
it  did  before ;  but  although  it  will  fall  rapidly  at  first,  it  will  continue 
to  fall  slowly  for  several  hours.  At  the  end  of  a  day,  if  the  temperature 
has  remained  constant,  it  will  show  a  depression  which  indicates  a 
vapor  pressure  of  the  ether  just  as  great  as  that  existing  in  a  tube 
which  contains  no  air. 

The  experiment  leads,  then,  to  the  rather  remarkable  con- 
clusion that  just  as  much  liquid  will  evaporate  into  a  space 
which  is  already  full  of  air  as  into  a  vacuum.  The  air  has 
no  effect  except  to  retard  greatly  the  rate  of  evaporation. 

207.  Explanation  of  the  retarding  influence  of  air  on  evapo- 
ration. This  retarding  influence  of  air  on  evaporation  is  easily 
explained  by  the  kinetic  theory ;  for  while  in  a  vacuum  the 
molecules  which  emerge  from  the  surface  fly  at  once  to  the 
top  of  the  vessel,  when  air  is  present  the  escaping  molecules 
collide  with  the  air  molecules  before  they  have  gone  any 
appreciable  distance  away  from  the  surface  (probably  less 
than  .00001  centimeter),  and  only  work  their  way  up  to  the 
top  after  an  almost  infinite  number  of  collisions.  Thus,  while 
the  space  immediately  above  the  liquid  may  become  saturated 
very  quickly,  it  requires  a  long  time  for  this  condition  of 
saturation  to  reach  the  top  of  the  vessel. 

QUESTIONS  AND  PROBLEMS 

1.  Account  for  the  evaporation  of  naphthaline  moth  balls  at  ordi- 
nary room  temperatures. 

2.  Why  do  clothes  dry  more  quickly  on  a  windy  day  than  on  a  quiet 
day? 

3.  If  the  inside  of  a  barometer  tube  is  wet  when  it  is  filled  with  mer- 
cury, will  the  height  of  the  mercury  be  the  same  as  in  a  dry  tube  ? 


HYGROMETRY  173 

4.  How  many  grams  of  water  will  evaporate  at  20°  C.  into  a  closed 
room  18  x  20  x  4  m.  ?    (See  table,  p.  171.) 

5.  At  a  temperature  of  15°  C.  what  will  be  the  error  in  the  baro- 
metric height  indicated  by  a  barometer  which  contains  moisture? 

6.  At  20°  C.  how  great  was  the  error  in  reading  due  to  the  presence 
of  water  vapor  in  Otto  von  Guericke's  barometer  ? 

HYGROMETRY,  OR  THE  STUDY  OF  MOISTURE  CONDITIONS 
IN  THE  ATMOSPHERE  * 

208.  Condensation  of  water  vapor  from  the  air.  Were  it  not 
for  the  retarding  influence  of  air  upon  evaporation  we  should 
be  obliged  to  live  in  an  atmosphere  which  would  be  always 
completely  saturated  with  water  vapor,  for  the  evaporation 
from  oceans,  lakes,  and  rivers  would  almost  instantly  saturate 
all  the  regions  of  the  earth.  This  condition  —  one  in  which 
moist  clothes  would  never  dry,  and  in  which  all  objects  would 
be  perpetually  soaked  in  moisture  —  would  be  exceedingly 
uncomfortable  if  not  altogether  unendurable. 

But  on  account  of  the  slowness  with  which,  as  the  last  ex- 
periment showed,  evaporation  into  air  takes  place,  the  water 
vapor  which  always  exists  in  the  atmosphere  is  usually  far 
from  saturated,  even  in  the  immediate  neighborhood  of  lakes 
and  rivers.  Since,  however,  the  amount  of  vapor  which  is 
necessary  to  produce  saturation  rapidly  decreases  with  a  fall 
in  temperature,  if  the  temperature  decreases  continually  in 
some  unsaturated  locality  it  is  clear  that  a  point  must  soon 
be  reached  at  which  the  amount  of  vapor  already  existing  in  a 
cubic  centimeter  of  the  atmosphere  is  the  amount  correspond- 
ing to  saturation.  Then,  if  the  temperature  still  continues  to 
fall,  the  vapor  must  begin  to  condense.  Whether  it  condenses 
as  dew  or  cloud  or  fog  or  rain  will  depend  upon  how  and 
where  the  cooling  takes  place. 

*  It  is  recommended  that  this  subject  be  preceded  by  a  laboratory  deter- 
mination of  dew  point,  humidity,  etc.  See,  for  example,  Experiment  10  of 
the  authors'  Manual. 


174  CHANGE  OF  STATE 

209.  The  formation  of  dew  and  frost.    If  the  cooling  is  due 
to  the  natural  radiation  of  heat  from  the  earth  at  night  after 
the  sun's  warmth  is  withdrawn,  the  atmosphere  itself  does  not 
fall  in  temperature  nearly  as  rapidly  as  do  solid  objects  on  the 
earth,  such  as  blades  of  grass,  trees,  stones,  etc.    The  layers  of 
air  which  come  into  immediate  contact  with  these  cooled  bodies 
are  themselves  cooled,  and  as  they  thus  reach  a  temperature 
at  which  the  amount  of  moisture  which  they  already  contain 
is  in  a  saturated  condition,  they  begin  to  deposit  this  mois- 
ture, in  the  form  of  dew  or  frost,  upon  the  cold  objects.    The 
drops  of  moisture  which  collect  on  an  ice  pitcher  in  summer 
illustrate   perfectly  the  formation  of  dew.     If  condensation 
takes  place  upon  a  surface  colder  than  the  freezing  temper- 
ature, frost  is  formed,  as  is  observed,  for  instance,  on  grass 
and  on  windowpanes. 

210.  The  formation  of  fog.    If  the  cooling  at  night  is  so 
great  as  not  only  to  bring  the  grass  and  trees  below  the  tem- 
perature at  which  the  vapor  in  the  air  in  contact  with  them  is 
in  a  state  of  saturation,  but  also  to  lower  the  whole  body  of 
air  near  the  earth  below  this  temperature,  then  the  condensa- 
tion takes  place  not  only  on  the  solid  objects  but  also  on  dust 
particles  suspended  in  the  atmosphere.    This  constitutes  a  fog. 

211.  The  formation  of  clouds,  rain,  sleet,  hail,  and  snow. 
When  the  cooling  of  the  atmosphere  takes  place  at  some  dis- 
tance above  the  earth's  surface,  as  when  a  warm  current  of 
air  enters  a  cold  region,  if  the  resultant  temperature  is  below 
that  at  which  the  amount  of  moisture  already  in  the  air  is 
sufficient  to  produce  saturation,  this  excessive  moisture  im- 
mediately condenses  about  floating  dust  particles  and  forms  a 
cloud.    If  the  cooling  is  sufficient  to  free  a  considerable  amount 
of  moisture,  the  drops  become  large  and  fall  as  rain.    If  this 
falling  rain  freezes  before  it  reaches  the  ground,  it  is  called 
sleet.    If  the  temperature  at  which  condensation  begins  is  be- 
low freezing,  the  condensing  moisture  forms  into  snouflakes. 


HYGROMETRY 


175 


When  the  violent  air  currents .  which  accompany  thunder- 
storms cany  the  condensed  moisture  up  and  down  several 
times  through  alternate  regions  of  snow  and  rain,  hailstones 
are  formed. 

212.  The  dew  point.    The  temperature  to  which  the  atmosphere 
must  be  cooled  in  order  that  condensation  of  the  water  vapor 
within  it  may  begin  is  called  the  dew  point."  This 
temperature  may  be  found  by  partly  filling  with 

water  a  brightly  polished  vessel  of  200  or  300 
cubic  centimeters  capacity  and  dropping  into  it 
little  pieces  of   ice,   stirring  thoroughly  at  the 
same    time  with  a  thermometer. 
The  dew  point  is  the  temperature 
indicated  by  the  thermometer  at 
the  instant  a  film  of  moisture  ap- 
pears upon  the  polished  surface. 
In  winter  the  dew  point  is  usually 
below  freezing,  and  it  will  there- 
fore be  necessary  to  add  salt  to  the 

ice  and  water  in  order  to  make  the  film  appear.  The  experi- 
ment may  be  performed  equally  well  by  bubbling  a  current  of 
air  through  ether  contained  in  a  polished  tube  (Fig.  174). 

213.  Humidity  of  the  atmosphere.    From  the  dew  point  and 
table  given  in  §  205,  p.  171,  we  can  easily  find  what  is  com- 
monly known  as  the  relative  humidity  or  the  degree  of  satura- 
tion of  the  atmosphere.    Relative  humidity  is  defined  as  the 
ratio  between  the  amount  of  moisture  per  cubic  centimeter  actu- 
ally present  in  the  air  and  the  amount  which  ivould  be  present  if 
the  air  were  completely  saturated.    This  is  precisely  the  same 
as  the  ratio  between  the  pressure  which  the  water  vapor  pres- 
ent in  the  air  exerts  and  the  pressure  which  it  would  exert 
if  it  were  present  in  sufficient  quantity  to  be  in  the  saturated 
condition.    An  example  will  make  clear  the  method  of  find- 
ing the  relative  humidity. 


FIG.  174.   Apparatus  for  deter- 
mining dew  point 


176  CHANGE  OF  STATE 

Suppose  that  the  dew  point  were  found  to  lye  15°  C.  on  a  day  on  whicli 
the  temperature  of  the  room  was  25°  C.  The  amount  of  moisture  actu- 
ally present  in  the  air  then  saturates  it  at  15°  C.  We  see  from  the  P 
column  in  the  table  that  the  pressure  of  saturated  vapor  at  15°  C.  is 
12.7  millimeters.  This  is,  then,  the  pressure  exerted  by  the  vapor  in  the 
air  at  the  time  of  our  experiment.  Running  down  the  table,  we  see  that 
the  amount  of  moisture  required  to  produce  saturation  at  the  tempera- 
ture of  the  room,  that  is,  at  25°,  would  exert  a  pressure  of  23.5  millimeters. 
Hence  at  the  time  of  the  experiment  the  air  contains  12.7/23.5,  or  .54, 
as  much  water  vapor  as  it  might  hold.  AVe  say,  therefore,  that  the  air 
is  54%  saturated,  or  that  the  relative  humidity  is  54%. 

214.  Practical  value  of  humidity  determinations.    From  hu- 
midity determinations  it  is  possible  to  obtain  much  information 
regarding  the  likelihood  of  rain  or  frost.    Such  observations 
are  continually  made  for  this  purpose  at  all  meteorological 
stations.    They  are  also  made  in  greenhouses,  to  see  that  the 
air  does  not  become  too  dry  for  the  welfare  of  the  plants, 
and  in  hospitals   and  public  buildings  and  even  in  private 
dwellings,  in  order  to  insure  the  maintenance  of  hygienic  liv- 
ing conditions.    For  the  most  healthful  conditions  the  relative 
humidity  should  be  kept  at  from  50%  to  60%. 

Low  relative  humidity  in  the  home  causes  discomfort  and 
colds,  and  leads  to  waste  of  fuel  estimated  at  from  10%  to 
25%.  The  average  home  heated  to  72°  F.  by  steam  or  hot 
water  is  estimated  by  health  authorities  to  have  a  relative  hu- 
midity of  30%,  and  even  as  little  as  25%  with  hot-air  heat- 
ing. This  is  less  than  the  average  humidity  of  extensive 
desert  regions.  Higher  humidity  in  the  home  would  diminish 
the  cooling  effect  due  to  rapid  evaporation  of  the  perspiration 
from  the  body,  and  would  make  us  feel  comfortable  if  a  lower 
temperature  were  maintained  (see  §  215). 

215.  Cooling  effect  of  evaporation.    Let  three  shallow  dishes  be 
partly  filled,  the  first  with  water,  the  second  with  alcohol,  and  the  third 
with  ether,  the  bottles  from  which  these  liquids  are  obtained  having  stood 
in  the  room  long  enough  to  acquire  its  temperature.    Let  three  students 


HYGKOMETKY  177 

carefully  read  as  maiiy  thermometers,  first  before  their  bulbs  have  been 
immersed  in  the  respective  liquids  and  then  after.  In  every  case  the 
temperature  of  the  liquid  in  the  shallow  vessel  will  be  found  to  be 
somewhat  lower  than  the  temperature  of  the  air,  the  difference  being 
greatest  in  the  case  of  ether  and  least  in  the  case  of  water. 

It  appears  from  this  experiment  that  an  evaporating  liquid 
assumes  a  temperature  somewhat  lower  than  its  surroundings, 
and  that  the  substances  which  evaporate  the  most  readily 
assume  the  lowest  temperatures. 

In  dry,  hot  climates  where  ice  is  not  readily  obtained  drink- 
ing water  is  frequently  kept  in  canvas  bags  or  unglazed  earth- 
enware. The  slow  evaporation  of  the  water  from  the  outside 
of  the  porous  container  keeps  the  water  within  quite  cool. 

Another  way  of  establishing  the  same  truth  is  to  place  a  few  drops 
of  each  of  the  above  liquids  in  succession  on  the  bulb  of  the  arrange- 
ment shown  in  Fig.  143  and  observe  the  rise  of  water  in  the  stem ;  or, 
more  simply  still,  to  place  a  few  drops  of  each  liquid  on  the  back  of 
the  hand  and  notice  that  the  order  in  which  they  evaporate  —  namely, 
ether,  alcohol,  water  —  is  the  order  of  greatest  cooling. 

In  twenty-four  hours  a  healthy  person  perspires  from  a  pint 
to  a  quart,  while  one  who  exercises  violently  may  perspire  a 
gallon  in  that  time. 

216.  Explanation  of  the  cooling  effect  of  evaporation.  The 
kinetic  theory  furnishes  a  simple  explanation  of  the  cooling 
effect  of  evaporation.  We  saw  that,  in  accordance  with  this 
theory,  evaporation  means  an  escape  from  the  surface  of 
those  molecules  which  have  acquired  velocities  considerably 
above  the  average.  But  such  a  continual  loss  of  the  most 
rapidly  moving  molecules  involves,  of  course,  a  continual 
diminution  of  the  average  velocity  of  the  molecules  left  behind, 
and  this  means  a  decrease  in  the  temperature  of  the  liquid. 

Again,  we  should  expect  the  amount  of  cooling  to  be  pro- 
portional to  the  rate  at  which  the  liquid  is  losing  molecules. 
Hence,  of  the  three  liquids  studied,  ether  should  cool  most 
rapidly,  since  it  evaporates  most  rapidly. 


178  CHANGE  OF  STATE 

217.  Freezing  by  evaporation.    In  §  206  it  was  shown  that 
a  liquid  will  evaporate  much  more  quickly  into  a  vacuum 
than  into  a  space  containing  air.    Hence,  if  we  place  a  liquid 
under  the  receiver  of  an  air  pump  and  exhaust  rapidly,  we 
ought   to  expect  a  much   greater  fall   in   temperature   than 
when   the  liquid   evaporates   into  air.    This  conclusion  may 
be  strikingly  verified  as  follows: 

Let  a  thin  watch  glass  be  filled  with  ether  and  placed  upon  a  drop 
of  cold  water,  preferably  ice  water,  which  rests  upon  a  thin  glass  plate. 
Let  the  whole  arrangement  be  placed  underneath  the  receiver  of  an  air 
pump  and  the  air  rapidly  exhausted.  After  a  few  minutes  of  pumping 
the  watch  glass  will  be  found  frozen  to  the  plate. 

By  evaporating  liquid  helium  in  this  way  Professor  Kara- 
erlingh  Onnes  of  Leyden,  in  1911,  attained  the  lowest  tem- 
perature that  had  ever  been  reached,  namely,  —271.3°  C. 
(  -  456.3°  F.),  less  than  2°  C.  above  absolute  zero. 

218.  Effect  of  air  currents  upon  evaporation.    Let  four  ther- 
mometer bulbs,  the  first  of  which  is  dry,  the  second  wetted  with  water, 
the  third  with  alcohol,  and  the  fourth  with  ether,  be  rapidly  fanned  and 
their  respective  temperatures  observed.    The  results  will  show  that  in 
all  of  the  wetted  thermometers  the  fanning  will  considerably  augment 
the  cooling,  but  the  dry  thermometer  will  be  wholly  unaffected. 

The  reason  why  fanning  thus  facilitates  evaporation,  and 
therefore  cooling,  is  that  it  removes  the  saturated  layers  of 
vapor  which  are  in  immediate  contact  with  the  liquid  and  re- 
places them  by  unsaturated  layers  into  which  new  evaporation 
may  at  once  take  place.  From  the  behavior  of  the  dry-bulb 
thermometer,  however,  it  will  be  seen  that  fanning  produces 
cooling  only  when  it  can  thus  hasten  evaporation.  A  dry  body 
at  the  temperature  of  the  room  is  not  cooled  in  the  slightest 
degree  by  blowing  a  current  of  air  across  it. 

219.  The   wet-   and   dry-bulb    hygrometer.      In   the   wet- 
and  dry-bulb  hygrometer  (Fig.  175)  the  principle  of  cooling 
by  evaporation  finds  a  very  useful  application.   This  instrument 


HYGKOMETRY 


179 


© 


consists  of  two  thermometers,  the  bulb  of  one  of  which  is  dry, 
while  that  of  the  other  is  kept  continually  moist  by  a  wick 
dipping  into  a  vessel  of  water.  Unless  the  air  is  saturated 
the  wet  bulb  indicates  a  lower  tempera- 
ture than  the  dry  one,  for  the  reason  that 
evaporation  is  continually  taking  place 
from  its  surface.  How  much  lower  will 
depend  on  how  rapidly  the  evaporation 
proceeds,  and  this  in  turn  will  depend 
upon  the  relative  humidity  of  the  atmos- 
phere. Thus,  in  a  completely  saturated 
atmosphere  no  evaporation  whatever  takes 
place  at  the  wet  bulb,  and  it  consequently 
indicates  the  same  temperature  as  the  dry 
one.  By  comparing  the  indications  of  this 
instrument  with  those  of  the  dew-point 
hygrometer  (Fig.  1 74)  tables  have  been 
constructed  which  enable  one  to  deter- 
mine at  once  from  the  readings  of  the 
two  thermometers  both  the  relative  humidity  and  the  dew 
point.  On  account  of  their  convenience  instruments  of  this 
sort  are  used  almost  exclusively  in  practical  work.  They  are 
not  very  reliable  unless  the  air  is  made  to 
circulate  about  the  wet  bulb  before  the 
reading  is  taken.  In  scientific  work  this  is 
always  done. 

220.  Effect  of  increased  surface  upon  evap- 
oration. Let  a  small  test  tube  containing  a  few 
drops  of  water  be  dipped  into  a  larger  tube  or  a 
small  glass  containing  ether,  as  in  Fig.  176,  and 
let  a  current  of  air  be  forced  rapidly  through  the 
ether  with  an  aspirator  in  the  manner  shown.  The  water  within  the 
tube  will  be  frozen  in  a  few  minutes,  if  the  aspirator  is  operated  vigor- 
ously. The  experiment  works  most  successfully  if  the  walls  of  the  test 
tube  are  quite  thin  and  the  walls  of  the  outer  vessel  fairly  thick.  Why  ? 


FIG.  175.  Wet-  and  dry- 
bulb  hygrometer 


FIG.  176.   Freezing 
water  by  the  evap- 
oration of  ether 


180  CHANGE  OF  STATE 

The  effect  of  passing  bubbles  through  the  ether  is  simply 
to  increase  enormously  the  evaporating  surface,  for  the  ether 
molecules  which  could  before  escape  only  at  the  upper  sur- 
face can  now  escape  into  the  air  bubbles  as  well. 

221.  Factors  affecting  evaporation.  The  above  results  may 
be  summarized  as  follows:  The  rate  of  evaporation  depends 
(1)  on  the  nature  of  the  evaporating  liquid ;  (2)  on  the 
temperature  of  the  evaporating  liquid ;  (3)  on  the  degree  of 
saturation  of  the  space  into  which  the  evaporation  takes  place  • 
(4)  on  the  density  of  the  air  or  other  gas  above  the  evaporating 
surface  ;  (5)  on  the  rapidity  of  the  circulation  of  the  air  above 
the  evaporating  surface ;  (6)  on  the  extent  of  the  exposed 
surface  of  the  liquid. 

QUESTIONS  AND  PROBLEMS 

1.  Why  do  spectacle  lenses  become  coated  with  mist  on  entering  a 
warm  house  on  a  cold  winter  day? 

2.  Does  dew  "fall"? 

3.  Why  are  icebergs  frequently  surrounded  with  fog? 

4.  Dew  will  not  usually  collect  on  a  pitcher  of  ice  water  standing 
in  a  warm  room  on  a  cold  winter  day.    Explain. 

5.  The  dew  point  in  a  room  was  found  to  be  8°  C.    What  was  the 
relative  humidity  if  the  temperature  of  the  air  was  10°  C.?    20°  C.? 
30°  C.  ?    (Consult  table,  p.  171.) 

6.  What  weight  of  water  is  contained  in  a  room  5x5x3  m.  if  the 
relative  humidity  is  60%  and  the  temperature  20°  C.  ?  (See  table,  p.  171.) 

7.  If  a  glass  beaker  and  a  porous  earthenware  vessel  are  filled  with 
equal  amounts  of  water  at  the  same  temperature,  in  the  course  of  a  few 
minutes  a  noticeable  difference  of  temperature  will  exist  between  the 
two  vessels.   Which  will  be  the  cooler,  and  why  ?  Will  the  difference  in 
temperature  between  the  two  vessels  be  greater  in  a  dry  or  in  a  moist 
atmosphere  ? 

8.  Why  will  an  open,  narrow-necked  bottle  containing  ether  not 
show  as  low  a  temperature  as  an  open  shallow  dish  containing  the 
same  amount  of  ether? 

9.  Why  is  the  heat  so  oppressive  on  a  very  damp  day  in  summer? 
10.   A  morning  fog  generally  disappears  before  noon.    Explain  the 

reason  for  its  disappearance. 


BOILING  181 

11.  What  becomes  of  the  cloud  which  you  see  about  a  blowing  loco- 
motive whistle  ?  Is  it  steam  ? 

12.  Explain  why  it  is  necessary  in  winter  to  add  moisture  to  the  air 
of  our  homes  to  maintain  proper  relative  humidity,  but  not  necessary  in 
the  summer. 

13.  What  factors  affecting  evaporation  are  illustrated  by  the  follow- 
ing :   (1)  a  wet  handkerchief  dries  faster  if  spread  out,  (2)  clothes  dry 
best  on  a  windy  day,  (3)  clothes  do  not  dry  rapidly  on  a  cold  day,  (4) 
clothes  dry  slowly  on  humid  days  ?    Explain  each  fact. 

BOILING  * 

222.  Heat  of  vaporization  defined.    The  experiments  per- 
formed  in   Chapter  IV,  Molecular  Motions,  led  us  to  the 
conclusion  that,  at  the  free  surface  of  any  liquid,  molecules 
frequently  acquire  velocities  sufficiently  high  to  enable  them 
to  lift  themselves  beyond  the  range  of  attraction  of  the  mole- 
cules of  the  liquid  and  to  pass  off  as  free  gaseous  molecules 
into  the  space  above.    They  taught  us,  further,  that  since  it  is 
only  such  molecules  as  have  unusually  high  velocities  which 
are  able  thus  to  escape,  the  average  kinetic  energy  of  the  mole- 
cules left  behind  is  continually  diminished  by  this  loss  from 
the  liquid  of  the  most  rapidly  moving  molecules,  and  conse- 
quently the  temperature  of  an  evaporating  liquid  constantly 
falls  until  the  rate  at  which  it  is  losing  heat  is  equal  to  the 
rate  at  which  it  receives  heat  from  outside  sources.    Evapora- 
tion, therefore,  always  takes  place  at  the  expense  of  the  heat 
energy  of  the  liquid.    The  number  of  calories  of  heat  which  dis- 
appear in  the  formation  of  one  gram  of  vapor  is  called  the  heat 
of  vaporization  of  the  liquid. 

223.  Heat  due  to  condensation.    When  molecules  pass  off 
from  the  surface  of  a  liquid,  they  rise  against  the  downward 

*  It  is  recommended  that  this  subject  be  accompanied  by  a  laboratory 
determination  of  the  boiling  point  of  alcohol  by  the  direct  method  and  by 
the  vapor-pressure  method,  and  that  it  be  followed  by  an  experiment  upon 
the  fixed  points  of  a  thermometer  and  the  change  of  boiling  point  with 
pressure.  See,  for  example,  Experiments  23  and  24  of  the  authors1  Manual. 


182 


CHANGE  OF  STATE 


forces  exerted  upon  them  by  the  liquid,  and  in  so  doing  ex 
change  a  part  of  their  kinetic  energy  for  the  potential  energy 
of  separated  molecules  in  precisely  the  same  way  in  which  a 
ball  thrown  upward  from  the  earth  exchanges  its  kinetic 
energy  in  rising  for  the  potential  energy  which  is  represented 
by  the  separation  of  the  ball  from  the  earth.  Similarly,  just 
as  when  the  ball  falls  back  it  regains  in  the  descent  all  of 
the  kinetic  energy  lost  in  the  ascent,  so  when  the  molecules 
of  the  vapor  reenter  the  liquid  they  must  regain  all  of  the 
kinetic  energy  which  they  lost  when  they  passed  out  of  the 
liquid.  We  may  expect,  therefore,  that  every  gram  of  steam 
which  condenses  will  generate  in  this  process  the  same  number 
of  calories  as  was  required  to  vaporize  it.  This  is  the  prin- 
ciple of  the  steam  heating  of  buildings,  by  which  the  heat 
energy  that  disappears  in  converting  the  water  in  the  boilers 
into  steam  is  generated  again  when  the  steam  condenses  to 
water  within  the  radiators. 

224.  Measurement  of  heat  of  vaporization.    To  find  accurately 

the  number  of  calories  expended  in  the  vaporization,  or  released  in  the 
condensation,  of  a  gram  of  water  at  100°  C.,  we  pass  steam  rapidly  for 
two  or  three  minutes  from  an  arrangement 
like  that  shown  in  Fig.  177  into  a  vessel 
containing,  say,  500  g.  of  water.  We  ob- 
serve the  initial  and  final  temperatures  and 
the  initial  and  final  weights  of  the  water. 
If,  for  example,  the  gain  in  weight  of  the 
water  is  16.5  g.,  we  know  that  16.5  g.  of 
steam  have  been  condensed.  If  the  rise  in 
temperature  of  the  water  is  from  10°  C.  to 
30° C.,  we  know  that  500  x  (30- 10)  =  10,000 
calories  of  heat  have  entered  the  water.  If 
x  represents  the  number  of  calories  given 
up  by  1  g.  of  steam  in  condensing,  then  the 
total  heat  imparted  to  the  water  by  the  con- 
densation of  the  steam  is  16.5  x  calories.  This  condensed  steam  is  at 
first  water  at  100°  C.,  which  is  then  cooled  to  30°  C.  In  this  cooling 


FIG.  177.    Heat  of  vaporiza- 
tion of  water 


BOILING  183 

process  it  gives  up  16.5  x  (100  —  30)  =  1155  calories.    Therefore,  equat- 
ing the  heat  gained  by  the  water  to  the  heat  lost  by  the  steam,  we  have 

10,000  =  16.5  x  +  1155,  or  x  =  536. 

This  is  the  method  usually  employed  for  finding  the  heat  of 
vaporization.  The  now  accepted  value  of  this  constant  is  536. 

225.  Boiling  temperature  defined.    If  a  liquid  is  heated  by 
means  of  a  flame,  it  will  be  found  that  there  is  a  certain  tem- 
perature above  which  it  cannot  be  raised,  no  matter  how  rapidly 
the  heat  is  applied.    This  is  the  temperature  which  exists  when 
bubbles  of  vapor  form  at  the  bottom  of  the  vessel  and  rise  to 
the  surface,  growing  larger  as  they  rise.    This  temperature  is 
commonly  called  the  boiling  temperature. 

But  a  second  and  more  exact  definition  of  the  boiling  point 
may  be  given.  It  is  clear  that  a  bubble  of  vapor  can  exist 
within  the  liquid  only  when  the  pressure  exerted  by  the  vapor 
within  the  bubble  is  at  least  equal  to  the  atmospheric  pressure 
pushing  down  on  the  surface  of  the  liquid;  for  if  the  pres- 
sure within  the  bubble  were  less  than  the  outside  pressure, 
the  bubble  would  immediately  collapse.  Therefore  the  boiling 
point  is  the  temperature  at  which  the  pressure  of  the  saturated 
vapor  first  becomes  equal  to  the  pressure  existing  outside. 

226.  Variation  of  the  boiling  point  with  pressure.    Since  the 
pressure  of  a  saturated  vapor  varies  rapidly  with  the  temper- 
ature, and  since  the  boiling  point  has  been  defined  as  the 
temperature  at  which  the  pressure  of  the  saturated  vapor  is 
equal  to  the  outside  pressure,  it  follows  that  the  boiling  point 
must  vary  as  the  outside  pressure  varies. 

Thus  let  a  round-bottomed  flask  be  half  filled  with  water  and  boiled. 
After  the  boiling  has  continued  for  a  few  minutes,  so  that  the  steam 
has  driven  out  most  of  the  air  from  the  flask,  let  a  rubber  stopper  be 
inserted  and  the  flask  removed  from  the  flame  and  inverted  as  shown 
in  Fig.  178.  The  temperature  will  fall  rapidly  below  the  boiling  point ; 
but  if  cold  water  is  poured  over  the  flask,  the  water  will  again  begin  to 
boil  vigorously,  for  the  cold  water,  by  condensing  the  steam,  lowers  the 


184 


CHANGE  OF  STATE 


FIG.  178.   Lowering  the 
boiling  point  by  dimin- 
ishing the  pressure 


pressure  within  the  flask,  and  thus  enables  the  water  to  boil  at  a  temper- 
ature lower  than  100°  C.  The  boiling  will  cease,  howe^7er,  as  soon  as 
enough  vapor  is  formed  to  restore  the  pressure. 
The  operation  may  be  repeated  many  times 

without  reheating. 

<* 

At  the  city  of  Quito,  Ecuador,  water 
boils  at  90°  C. ;  on  the  top  of  Mt.  Blanc 
it  boils  at  84°  C. ;  and  on  Pikes  Peak, 
at  89°  C.  On  the  other  hand,  in  the 
boiler  of  a  locomotive  on  which  the 
gauge  records  a  pressure  of  250  pounds, 
as  is  frequently  the  case,  the  boiling  point 
of  the  water  is  208°  C.  (406°  F.). 

Closed  boilers  provided  with  safety  valves  (see  (7,  Fig.  179) 
and  known  as  digesters  are  used  for  more  rapid  cooking  in 
mountainous  regions.  Indeed,  a  temperature  only  a  few  de- 
grees above  100°  C.  causes  starch  grains  to  burst  open  much 
more  rapidly  than  does  a  temperature  of 
100°  C.  Large  digesters  are  used  in  ex- 
tracting gelatin  from  bones  and  in  reclaim- 
ing valuable  fatty  substances  at  garbage 
plants.  In  the  cold-pack  method  of  pre- 
serving fruits  and  vegetables  the  final 
sterilizing  is  done  by  placing  the  jars  or 
cans  in  closed  boilers  known  as  steam- 


FIG.  179.     A   closed 
boiler  for  family  use 


pressure  canners.* 

227.  Evaporation  and  boiling.  The  only 
essential  difference  between  evaporation 
and  boiling  is  that  the  former  consists  in  the  passage  of 
molecules  into  the  vaporous  condition  from  the  free  surface 
only,  while  the  latter  consists  in  the  passage  of  the  molecules 
into  the  vaporous  condition  both  at  the  free  surface  and  at 


*  Farmers'1  Bulletin  No.  839,  on  steam-pressure  canning,  may  be  obtained 
from  the  United  States  Department  of  Agriculture,  Washington,  D.  C. 


BOILING 


185 


the  surface  of  bubbles  which  exist  within  the  body  of  the 
liquid.  The  only  reason  why  vaporization  takes  place  so  much 
more  rapidly  at  the  boiling  temperature  than  just  below  it 
is  that  the  evaporating  surface  is  enormously  increased  as 
soon  as  the  bubbles  form.  The  reason  why  the  temperature 
cannot  be  raised  above  the  boiling  point  is  that  the  surface 
always  increases,  on  account  of  the  bubbles,  to  just  such  an 
extent  that  the  loss  of  heat  because  of  evaporation  is  exactly 
equal  to  the  heat  received  from  the  fire. 

228.  Distillation.    Let  water  holding  in  solution  some  aniline  dye 
be  boiled  in  B  (Fig.  180).    The  vapor  of  the  liquid  will  pass  into  the 
tube  T,  where  it  will  be  condensed 

by  the  cold  water  which  is  kept  in 
continual  circulation  through  the 
jacket  /.  The  condensed  water  col- 
lected in  P  will  be  seen  to  be  free 
from  all  traces  of  the  color  of  the 
dissolved  aniline. 

We  learn,  then,  that  when 
solids  are  dissolved  in  liquids,  the 
vapor  which  rises  from  the  solu- 
tion contains  none  of  the  dissolved 

substance.  Sometimes  it  is  the  pure  liquid  in  P  which  is 
desired,  as  in  the  manufacture  of  alcohol,  and  sometimes 
the  solid  which  remains  in  B,  as  in  the  manufacture  of 
sugar.  In  the  white-sugar  industry  it  is  necessary  that  the 
evaporation  take  place  at  a  low  temperature,  so  that  the 
sugar  may  not  be  scorched.  Hence  the  boiler  is  kept  par- 
tially exhausted  by  means  of  an  air  pump,  thus  enabling 
the  solution  to  boil  at  considerably  reduced  temperatures. 

229.  Fractional  distillation.  When  bo'th  of  the  constituents 
of  a  solution  are  volatile,  as  in  the  case  of  a  mixture  of  alcohol 
and  water,  the  vapor  of  both  will  rise  from  the  liquid.    But 
the  one  which  has  the  lower  boiling  point,  that  is,  the  higher 


FIG.  180.    Distillation 


186  CHANGE  OF  STATE 

vapor  pressure,  will  predominate.  Hence,  if  we  have  in  B 
(Fig.  180)  a  solution  consisting  of  50%  alcohol  and  50% 
water,  it  is  clear  that  we  can  obtain  in  P,  by  evaporating 
and  condensing,  a  solution  containing  .a  much  larger  percent- 
age of  alcohol.  By  repeating  this  operation  a  number  of  times 
we  can  increase  the  purity  of  the  alcohol.  This  process  is 
called  fractional  distillation.  The  boiling  point  of  the  mixture 
lies  between  the  boiling  points  of  alcohol  and  water,  being 
higher  the  greater  the  percentage  of  water  in  the  solution. 
Gasoline  and  kerosene  are  separated  from  crude  oil,  and 
different  grades  of  gasoline  are  separated  from  each  other  by 
fractional  distillation. 

QUESTIONS  AND  PROBLEMS 

1.  A  fall  of  1°  C.  in  the  boiling  point  is  caused  by  rising  960  ft. 
How  hot  is  boiling  water  at  Denver,  5000  ft.  above  sea  level? 

2.  How  may  we  obtain  pure  drinking  water  from  sea  water  ? 

3.  After  water  has  been  brought  to  a  boil,  will  eggs  become  hard 
any  quicker  when  the  flame  is  high  than  when  it  is  low  ? 

4..  The  hot  water  which  leaves  a  steam  radiator  may  be  as  hot  as 
the  steam  which  entered  it.    How,  then,  has  the  room  been  warmed  ? 

5.  In  a  vessel  of  water  which  is  being  heated  fine  bubbles  rise  long 
before  the  boiling  point  is  reached.    Why  is  this  so  ?    How  can  you  dis- 
tinguish between  this  phenomenon  and  boiling  ? 

6.  When  water  is  boiled  in  a  deep  vessel,  it  will  be  noticed  that  the 
bubbles  rapidly  increase  in  size  as  they  approach  the  surface.    Give  two 
reasons  for  this. 

7.  Why  are  burns  caused  by  steam  so  much  more  severe  than  burns 
caused  by  hot  water  of  the  same  temperature  ? 

8.  How  many  times  as  much  heat  is  required  to  convert  any  body 
of  boiling  water  into  steam  as  to  warm  an  equal  weight  of  water  1°  C.? 

9.  How  many  B.  T.  U.  are  liberated  within  a  radiator  when  10  Ib. 
of  steam  condense  there  ? 

10.  In  a  certain  radiator  2  kg.  of  steam  at  100°  C.  condensed  to  water 
in  1  hr.  and  the  water  left  the  radiator  at  90°  C.    How  many  calories 
were  given  to  the  room  during  the  hour? 

11.  How  many  calories  are  given  up  by  30  g.  of  steam  at  100°  C.  in 
condensing  and  then  cooling  to  20°  C.  ?  How  much  water  will  this  steam 
raise  from  10°  C.  to  20°  C.? 


ARTIFICIAL  COOLING  187 

ARTIFICIAL  COOLING 

230.  Cooling  by  solution.    Let  a  handful  of  common  salt  be  placed 
in  a  small  beaker  of  water  at  the  temperature  of  the  room  and  stirred 
with  a  thermometer.  The  temperature  will  fall  several  degrees.    If  equal 
weights  of  ammonium  nitrate  and  water  at  15°  C.  are  mixed,  the  tem- 
perature will  fall  as  low  as  —  10°  C.    If  the  water  is  nearly  at  0°  C.  when 
the  ammonium  nitrate  is  added,  and  if  the  stirring  is  done  with  a  test 
tube  partly  filled  with  ice-cold  water,  the  water  in  the  tube  will  be  frozen. 

These  experiments  show  that  the  breaking  up  of  the  crystals 
of  a  solid  requires  an  expenditure  of  heat  energy,  as  well  when 
this  operation  is  effected  by  solution  as  by  fusion.  The  reason 
for  this  will  appear  at  once  if  we  consider  the  analogy  between 
solution  and  evaporation  ;  for  just  as  the  molecules  of  a  liquid 
tend  to  escape  from  its  surface  into  the  air,  so  the  molecules  at 
the  surface  of  the  salt  are  tending,  because  of  their  velocities, 
to  pass  off,  and  are  only  held  back  by  the  attractions  of  the 
other  molecules  in  the  crystal  to  which  they  belong.  If,  how- 
ever, the  salt  is  placed  in  water,  the  attraction  of  the  water 
molecules  for  the  salt  molecules  aids  the  natural  velocities  of 
the  latter  to  carry  them  beyond  the  attraction  of  their  fellows. 
As  the  molecules  escape  from  the  salt  crystals  two  forces  are 
acting  on  them,  the  attraction  of  the  water  molecules  tending 
to  increase  their  velocities,  and  the  attraction  of  the  remaining 
salt  molecules  tending  to  diminish  these  velocities.  If  the 
latter  force  has  a  greater  resultant  effect  than  the  former,  the 
mean  velocity  of  the  molecules  after  they  have  escaped  will 
be  diminished  and  the  solution  will  be  cooled.  But  if  the 
attraction  of  the  water  molecules  amounts  to  more  than  the 
backward  pull  of  the  dissolving  molecules,  as  when  caustic 
potash  or  sulphuric  acid  is  dissolved,  the  mean  molecular 
velocity  is  increased  and  the  solution  is  heated. 

231.  Freezing  points  of  solutions.    If  a  solution  of  one  part 
of  common  salt  to  ten  of  water  is  placed  in  a  test  tube  and 
immersed  in  a  "  freezing  mixture  "  of  water,  ice,  and  salt,  the 


188  CHANGE  OF  STATE 

temperature  indicated  by  a  thermometer  in  the  tube  will  not  be 
zero  when  ice  begins  to  form,  but  several  degrees  below  zero. 
The  ice  which  does  form,  however,  will  be  found,  like  the  vapor 
which  rises  above  a  salt  solution,  to  be  free  from  salt,  and  it  is 
this  fact  which  furnishes  a  key  to  the  explanation  of  why  the 
freezing  point  of  the  salt  solution  is  lower  than  that  of  pure 
water.  For  cooling  a  substance  to  its  freezing  point  simply 
means  reducing  its  temperature,  and  therefore  the  mean  ve- 
locity of  its  molecules,  sufficiently  to  enable  the  cohesive  forces 
of  the  liquid  to  pull  the  molecules  together  into  the  crystalline 
form.  Since  in  the  freezing  of  a  salt  solution  the  cohesive 
forces  of  the  water  are  obliged  to  overcome  the  attractions 
of  the  salt  molecules  as  well  as  the  molecular  motions,  the 
motions  must  be  rendered  less,  that  is,  the  temperature  must 
be  made  lower,  than  in  the  case  of  pure  water  in  order  that 
crystallization  may  occur.  From  this  reasoning  we  should  ex- 
pect that  the  larger  the  amount  of  salt  in  solution  the  lower 
would  be  the  freezing  point.  This  is  indeed  the  case.  The 
lowest  freezing  point  obtainable  with  common  salt  in  water  is 
—  22°  C.,  or  —  7.6°  F.  This  is  the  freezing  point  of  a  saturated 
solution. 

232.  Freezing  mixtures.  If  snow  or  ice  is  placed  in  a  vessel 
of  water,  the  water  melts  it,  and  in  so  doing  its  temperature  is 
reduced  to  the  freezing  point  of  pure  water.  Similarly,  if  ice 
is  placed  in  salt  water,  it  melts  and  reduces  the  temperature  of 
the  salt  water  to  the  freezing  point  of  the  solution.  This  may 
be  one,  or  two,  or  twenty-two  degrees  below  zero,  according 
to  the  concentration  of  the  solution.  Therefore,  whether  we 
put  the  ice  in  pure  water  or  in  salt  water,  enough  of  it  always 
melts  to  reduce  the  whole  mass  to  the  freezing  point  of  the 
liquid,  and  each  gram  of  ice  which  melts  uses  up  80  calories 
of  heat.  The  efficiency  of  a  mixture  of  salt  and  ice  in  producing 
cold  is  therefore  due  simply  to  the  fact  that  the  freezing  point  of 
a  salt  solution  is  lower  than  that  of  pure  water. 


INDUSTRIAL  APPLICATIONS  189 

The  best  proportions  are  three  parts  of  snow  or  finely 
shaved  ice  to  one  part  of  common  salt.  If  three  parts  of 
calcium  chloride  are  mixed  with  two  parts  of  snow,  a  tem- 
perature of  —  55°  C.  may  be  produced.  This  is  low  enough 
to  freeze  mercury. 

QUESTIONS  AND  PROBLEMS 

1.  When  salt  water  freezes,  the  ice  formed  is  free  from  salt.    What 
effect,  then,  does  freezing  have  on  the  concentration  of  a  salt  solution  ? 

2.  A  partially  concentrated  salt  solution  which  has  a  freezing  point  of 
—  5°  C.  is  placed  in  a  room  which  is  kept  at  —  10°  C.    Will  it  all  freeze  ? 

3.  Explain  why  salt  is  thrown  on  icy  sidewalks  on  cold  winter  days. 

4.  Give  two  reasons  why  the  ocean  freezes  less  easily  than  the  lakes. 

5.  Why  does  pouring  H2SO4  into  water  produce  heat,  while  pouring 
the  same  substance  upon  ice  produces  cold? 

6.  Why  will  a  liquid  which  is  unable  to  dissolve  a  solid  at  a  low 
temperature  often  do  so  at  a  higher  temperature  ?  (See  §  230.) 

7.  When  the  salt  in  an  ice-cream  freezer  unites  with  the  ice  to  form 
brine,  about  how  many  calories  of  heat  are  used  for  each  gram  of  ice 
melted  ?    Where  does  it  come  from  ?    If  the  freezing  point  of  the  salt 
solution  were  the  same  as  that  of  the  cream,  would  the  cream  freeze  ? 

INDUSTRIAL  APPLICATIONS 

233.  The  modern  steam  engine.  Thus  far  in  our  study  of 
the  transformations  of  energy  we  have  considered  only  cases 
in  which  mechanical  energy  was  transformed  into  heat  energy. 
In  all  heat  engines  we  have  examples  of  exactly  the  reverse 
operation,  namely,  the  transformation  of  heat  energy  back  into 
mechanical  energy.  'How  this  is  done  may  best  be  understood 
from  a  study  of  various  modern  forms  of  heat  engines.  The 
invention  of  the  form  of  the  steam  engine  which  is  now  in  use 
is  due  to  James  Watt,  who,  at  the  time  of  the  invention  (1768), 
was  an  instrument  maker  in  the  University  of  Glasgow. 

The  operation  of  such  a  machine  can  best  be  understood 
from  the  ideal  diagram  shown  in  Fig.  181.  Steam  generated 
in  the  boiler  B  by  the  fire  F  passes  through  the  pipe  S  into 


190 


CHANGE  OF  STATE 


the  steam  chest  V,  and  thence  through  the  passage  N  into  the 
cylinder  (7,  where  its  pressure  forces  the  piston  P  to  the  left. 
It  will  be  seen  from  the  figure  that  as  the  driving  rod  R 
moves  toward  the  left  the  so-called  eccentric  rod  R',  which 
controls  the  valve  P7,  moves  toward  the  right.  Hence,  when 
the  piston  has  reached  the  left  end  of  its  stroke,  the  passage 


FIG.  181.   Ideal  diagram  of  a  steam  engine 

N  will  have  been  closed,  while  the  passage  M  will  have  been 
opened,  thus  throwing  the  pressure  from  the  right  to  the  left 
side  of  the  piston,  and  at  the  same  time  putting  the  right  end  of 
the  cylinder,  which  is  full  of  spent  steam,  into  connection  with 
the  exhaust  pipe  E.  This  operation  goes  on  continually,  the  rod 
R'  opening  and  closing  the  passages  M  and  ^Vat  just  the  proper 
moments  to  keep  the  piston  moving  back  and  forth  through- 
out the  length  of  the  cylinder.  The  shaft  carries  a  heavy 
flywheel  W,  the  great  inertia  of  which  insures  constancy  in 
speed.  The  motion  of  the  shaft  is  communicated  to  any 


i!  ill 


THE  LIBERTY  MOTOR 

This  400-horse-power  motor,  one  of  America's  important  contributions  to  the  World 
War,  was  developed  for  use  on  the  larger  types  of  bombing  airplanes.  It  makes 
1700  revolutions  per  minute  and  has  twelve  cylinders,  which  are  water-cooled. 
It  weighs  806  pounds,  or  about  2  pounds  per  horse  power.  The  NC-4,  which  made 
the  first  transatlantic  flight,  was  equipped  with  three  of  these  motors 


INDUSTEIAL  APPLICATIONS 


191 


desired  machinery  by  means  of  a  belt  which  passes  over  the 
pulley  W.  Within  the  boiler  the  steam  is  at  high  pressure 
and  high  temperature  (§  226).  The  steam  falls  in  temperature 
within  the  cylinder  while  doing  the  work  of  pushing  the  piston. 
A  steam  engine  is  a  mechanical  device  ivhich  accomplishes  useful 
work  by  transforming  heat  energy  into  mechanical  energy. 

234.  Condensing  and  noncondensing  engines.     In  most  sta- 
tionary engines  the  exhaust  E  leads  to  a  condenser  which 
consists  of  a  chamber  Q,  into  which  plays  a  jet  of  cold  water 
T,  and  in  which  a  partial  vacuum  is  maintained  by  means  of 
an  air  pump.     In  the  best  engines  the  pressure  within  Q  is 
not  more  than  from  3  to  5  centimeters  of  mercury,  that  is, 
not  more  than  a  pound  to  the  square  inch.     Hence  the  con- 
denser reduces  the  back   pressure  against  that  end  of  the 
piston   which  is   open   to   the   atmosphere   from   15   pounds 
down  to  1  pound,  and  thus  increases  the  effective  pressure 
which  the  steam  on  the  other  side  of  the  piston  can  exert. 

235.  The  eccentric.    In  practice  the  valve  rod  R'  is  not  attached  as  in 
the  ideal  engine  indicated  in  Fig.  181,  but  motion  is  communicated  to 
it   by    a    so-called    ec- 
centric.   This  consists 

of  a  circular   disk   K 

(Fig.  182)  rigidly    at- 

tached  to  the  axle  but 

so  set  that  its  center 

does  not  coincide  with 

the  center  of  the  axle 

A.   The  disk  # rotates 

inside  the  collar  C  and 

thus  communicates  to  FTG>  182.   The  eccentric 

the  eccentric  rod  R'  a 

back-and-forth  motion  which  operates  the  valve  V  in  such  a  way  as 

to  admit    steam    alternately   through   M  and  N  at  the   proper  time. 

236.  The  boiler.   When  an  engine  is  at  work,  steam  is  being  removed 
very  rapidly  from  the  boiler  ;  for  example,  a  railway  locomotive  consumes 
from  3  to  fi  tons  of  water  per  hour.    Tt  is  therefore  necessary  to  have 


192 


CHANGE  OF  STATE 


the  fire  in  contact  with  as  large  a  surface  as  possible.  In  the  tubular 
boiler  this  end  is  accomplished  by  causing  the  flames  to  pass  through 
a  large  number  of  metal  tubes  immersed  in  water.  The  arrangement 


FIG.  183.    Diagram  of  locomotive 

of  the  furnace  and  the  boiler  may  be  seen  from  the  diagram  of  a  loco- 
motive shown  in  Fig.  183.  (See  early  and  modern  types  opposite  p.  123.) 

237.  The  draft.    In  order  to  force  the  flames  through  the  tubes  B  of 
the  boiler  a  powerful  draft  is  required.    In  locomotives  this  is  obtained 
by  running  the  exhaust  steam  from  the  cylinder  C  (Fig.  183)  into  the 
smokestack  E  through  the  blower  F.   The  strong 

current  through  F  draws  with  it  a  portion  of  the 
air  from  the  smoke  box  Z),  thus  producing  within 
D  a  partial  vacuum  into  which  a  powerful  draft 
rushes  from  the  furnace  through  the  tubes  B.  The 
coal  consumption  of  an  ordinary  locomotive  is  from 
one-fourth  ton  to  one  ton  per  hour. 

In  stationary  engines  a  draft  is  obtained  by  mak- 
ing the  smokestack  very  high.  Since  in  this  case 
the  pressure  which  is  forcing  the  air  through  the 
furnace  is  equal  to  the  difference  in  the  weights  of 
columns  of  air  of  unit  cross  section  inside  and  outside  the  chimney,  it 
is  evident  that  this  pressure  will  be  greater  the  greater  the  height  of 
the  smokestack.  This  is  the  reason  for  the  immense  heights  given  to 
chimneys  in  large  power  plants. 

238.  The  governor.    Fig.  184  shows  an  ingenious  device  of  Watt's, 
called  a  governor,  for  automatically  regulating  the  speed  with  which  a 
stationary  engine  runs.    If  it  runs  too  fast,  the  heavy  rotating  balls  B 


FIG.  184.     The 
governor 


INDUSTRIAL  APPLICATIONS 


193 


move  apart  and  upward  and  in  so  doing  operate  a  valve  which  reduces 
the  speed  by  partially  shutting  off  the  supply  of  steam  from  the  cylinder. 
239.  Compound  engines.  In  an  engine  which  has  but  a  single  cylin- 
der the  full  force  of  the  steam  has  not  been  spent  when  the  cylinder 
is  opened  to  the  exhaust.  The  waste  of  energy  which  this  entails  is 
obviated  in  the  compound  engine 
(see  Fig.  311)  by  allowing  the 
partially  spent  steam  to  pass 
into  a  second  cylinder  of  larger 
area  than  the  first.  The  most 
efficient  of  modern  engines  have 
three  and  sometimes  four  cylin- 
ders of  this  sort,  and  the  en- 
gines are  accordingly  called  triple 
or  quadruple  expansion  engines. 


FIG.  185.    Cross-compound  engine 
cylinders 


Fig.  185  shows  the  relation  be- 
tween any  two  successive  cylin- 
ders of  a  cross-compound  engine. 
By  automatic  devices  not  differing  in  principle  from  the  eccentric,  valves 
C1,  D2,  and  E2  open  simultaneously  and  thus  permit  steam  from  the 
boiler  to  enter  the  small  cylinder  A,  while  the  partially  spent  steam  in 
the  other  end  of  the  same  cylinder  passes  through  D2  into  B,  and  the 
more  fully  exhausted  steam  in  the  upper  end  of  B  passes  out  through 
E2.  At  the  upper  end  of  the  stroke  of  the  pistons  P  and  P',  C1,  D2,  and 
E2  automatically  close,  while  C2,  D\  and  E1  simultaneously  open  and 
thus  reverse  the  direction  of  motion  of  both  pistons.  These  pistons  are 
attached  to  the  same  shaft. 

240.  Efficiency  of  a  steam  engine.  We  have  seen  that  it  is 
possible  to  transform  completely  a  given  amount  of  mechani- 
cal energy  into  heat  energy.  This  is  done  whenever  a  moving 
body  is  brought  to  rest  by  means  of  a  frictional  resistance. 
But  the  inverse  operation,  namely,  that  of  transforming  heat 
energy  into  mechanical  energy,  differs  in  this  respect,  that  it 
is  only  a  comparatively  small  fraction  of  the  heat  developed 
by  combustion  which  can  be  transformed  into  work.  For  it  is 
not  difficult  to  see  that  in  every  steam  engine  at  least  a  part 
of  the  heat  must  of  necessity  pass  over  with  the  exhaust  steam 
into  the  condenser  or  out  into  the  atmosphere.  This  loss  is  so 


194 


CHANGE  OF  STATE 


great  that  even  in  an  ideal  engine  not  more  than  about  23% 
of  the  heat  of  combustion  could  be  transformed  into  work.  In 
practice  the  very  best  condensing  engines  of  the  quadruple- 
expansion  type  transform  into  mechanical  work  not  more  than 
17%  of  the  heat  of  combustion.  Ordinary  locomotives  utilize 
at  most  not  more  than  8%.  The  efficiency  of  a  heat  engine  is 
defined  as  the  ratio  between  the  heat  utilized,  or  transformed  into 
work,  and  the  total  heat  expended.  The  efficiency  of  the  best 
steam  engines  is  therefore  about  -|^,  or  75%,  of  that  of  an 
ideal  heat  engine,  while  that  of  the  ordinary  locomotive  is 
only  about  ^-,  or  26%,  of  the  ideal  limit. 

241.  Principle  of   the  internal-combustion  engine.    Let  two 

iron  or  steel  wires  be  pushed  through  a  cork  stopper  and  their  ends  * 
brought  near  together  (1/32  inch  will  do) 
(Fig.  186).  With  an  atomizer  spray  into  the 
bottle  a  small  amount  of  benzine  or  gasoline 
(the  amount  to  use  can  be  determined  by 
trial),  insert  the  stopper,  and  bring  the  tips 
of  the  heavily  insulated  wires  leading  from  an 
induction  coil  to  the  underside  of  the  wires 
a,  b.  A  spark  will  pass  at  s ;  and,  if  the  mix- 
ture is  not  too  "  rich  "  or  too  "  lean,"  a  violent 
explosion  will  occur,  throwing  the  stopper  as 
high  as  the  ceiling.  (A  heavy  round  bottle  must 
be  used  for  safety.  Wrap  it  well  in  wire  gauze.) 

Within    the    last    two    decades   gas 

engines  have  become  quite  as  important  a  factor  in  modern 
life  as  steam  engines.  (See  opposite  pp.  190,  191,  and  198.) 
Such  engines  are  driven  by  properly  timed  explosions  of  a 
mixture  of  gas  and  air  occurring  within  the  cylinder. 

Fig.  187  is  a  diagram  illustrating  the  four  stages  into 
which  it  is  convenient  to  divide  the  complete  cycle  of  opera- 
tions which  goes  on  within  such  an  engine.  Suppose  that 
the  heavy  flywheel  W  has  already  been  set  in  motion.  As  the 
piston  p  moves  down  in  the  first  stroke  (see  1)  the  valve  D 


FIG.  186.    A  mixture  of 

gasoline    vapor   and    air 

will  explode 


INDUSTRIAL  APPLICATIONS 


195 


FIG.  187.    Principle  of  the  gas  engine 


opens  and  an  explosive  mixture  of  gas  and  air  is  drawn  into  the 

cylinder  through  D.   As  the  piston  rises  (see  2)  valve  D  closes, 

and  the  mixture  of  gas  and 

air   is   compressed    into    a 

small  space   in   the   upper 

end  of  the   cylinder.     An 

electric    spark   ignites   the 

explosive  mixture,  and  the 

force  of  the  explosion  drives 

the  piston  violently  down 

(see  3}.   At  the  besrirmintj 

\  y  o  o 

of  the  return  stroke  (see  4) 

the  exhaust  valve  E  opens,     ;\  w  }     \w  j     \  w 
and   as  the    piston  moves 
up,  the  spent  gaseous  prod- 
ucts of  the  explosion  are  forced  out  of  the  cylinder.    The  initial 
condition  is  thus  restored  and  the  cycle  begins  over  again. 

Since  it  is  only  during  the  third  stroke  that  the  engine  is 
receiving  energy  from  the  exploding  gas,  the  flywheel  is 
always  made  very  heavy  so  that  the  energy  stored  up  in  it 
in  the  third  stroke  may  keep  the  machine  running  with  little 
loss  of  speed  during  the  other  three  parts  of  the  cycle. 

The  efficiency  of  the  gas  engine  is  often  as  high  as  25%,  or  nearly 
double  that  of  the  best  steam  engines.  Furthermore,  it  is  free  from 
smoke,  is  very  compact,  and  may  be  started  at  a  moment's  notice.  On 
the  other  hand,  the  fuel  (gas  or  gasoline)  is  comparatively  expensive. 
Most  automobiles  are  run  by  gasoline  engines,  chiefly  because  the 
lightness  of  the  engine  and  of  the  fuel  to  be  carried  are  here  considera- 
tions of  great  importance. 

It  has  been  the  development  of  the  light  and  efficient  gas  engine 
which  has  made  possible  man's  recent  conquest  of  the  air  through  the 
use  of  the  airplane  and  airship. 

242.  The  automobile.  The  plate  opposite  page  198  shows 
the  principal  mechanical  features  of  the  automobile  in  their 
relation  to  one  another.  It  will  be  seen  that  the  cylinders 


196 


CHANGE  OF  STATE 


of  the  engine  are  surrounded 
by  water  jackets  which  form 
part  of  a  circulating  system. 
The  heat  of  the  engine  is  car- 
ried by  convection  currents  in 
this  water  to  the  radiator, 
where  it  is  lost  to  the  atmos- 
phere through  the  air  currents 
produced  in  part  by  a  revolving 
fan  (10).  Unless  some  means 
were  provided  for  cooling  a  gas 
engine,  it  would  become  so  over- 
heated that  the  pistons  would 
stick  fast.  The  power  of  the 
engine  is  transmitted  to  the  rear 
axle  through  the  clutch  (11), 
the  transmission  (12),  and  the 
differential  gearing. 

243.  The  clutch  and  the  transmis- 
sion. Since  a  gas  engine  develops 
its  power  by  a  series  of  violent  ex- 
plosions within  the  cylinders,  it  is 
clear  that  it  cannot  start  with  a  load 
as  does  the  steam  engine.  In  start- 
ing an  automobile  it  is  first  necessary 
that  the  engine  acquire  a  reasonable 
speed  and  that  the  power  be  applied 
gradually  to  the  rear  axle  by  the  use 
of  a  friction  clutch  (11);  otherwise 
the  engine  will  stall.  The  shaft  of 
the  engine  has  upon  its  rear  .end  a 
flywheel  which,  in  the  cone  clutch,  is 
turned  to  a  conical  shape  inside. 
Close  to  this  but  attached  to  the 
transmission  shaft  is  the  clutch  plate, 
a  heavy  disk  faced  with  leather,  which 


Rear 
(Transmission  Shaft] l|f 


Countershaft 


Neutral 


Firxt  (Low  Speed)  2 


Second  (Intermediate  Speed) 


FIG.  188.   Automobile  transmission 


INDUSTRIAL  APPLICATIONS 


197 


fits  the  inside  of  the  flywheel  and  is  pressed  into  it  by  a  spring  suffi- 
ciently strong  to  prevent  any  slipping  when  the  clutch  is  engaged. 
The  driver  throws  out  the  clutch  by  depressing  a  lever  with  his  foot. 
In  the  disk  clutch  the  bearing  surfaces  are  two  series  of  disks,  one 
revolving  with  the  engine  shaft,  the  other  with  the  transmission. 

The  amount  of  work  done  by  a  gas  engine  in  a  minute  depends  upon 
the  work  done  by  each  explosion  multiplied  by  the  number  of  explosions 
per  minute.  Therefore  it  can  develop  its  full  power  only  while  revolving 
rapidly.  In  hill  climbing,  for  example,  the  speed  of  the  engine  must  be 
great  while  that  of  the  car  is  comparatively  small.  To  meet  this  require- 
ment a  system  of  reduction  gears  called  the  transmission  (12)  is  used 
to  make  the  number  of  revolutions  of  the  driving  shaft  less  than  that 
of  the  crank  shaft  (4)  of  the  engine.  In  Fig.  188,  (1),  the  gears  are  in 
neutral,  gears  1  and  #  being  always  in  mesh.  By  use  of  the  gear-shift 
lever  (14)  gears  3  and  5  (Fig.  188)  are  made  to  slide  upon  a  square 
shaft.  Before  shifting  the  gears  the  clutch  is  released  to  disconnect  the 
power  of  the  motor  from  the  driving  shaft ;  and,  to  avoid  a  clash  when 
meshing  the  gears  on  the  transmission  shaft  with  those  on  the  counter- 
shaft, care  should  be  taken  that  they  revolve  at  about  the  same  speed. 
Fig.  188,  (2),  shows  the  low-speed  connection.  In  shifting  to  second  speed 
(Fig.  188,  (#))  the  clutch  is  released,  gear  5  is  thrown  into  neutral,  and 
finally  gear  3  is  meshed  with  4,  after  which 
the  clutch  is  allowed  to  grip.  In  going 
to  high  speed  (Fig.  188,  (4))  gear  3  is 
shifted  through  neutral  to  engagement 
with  gear  1.  This  connects  the  crank  shaft 
of  the  engine  directly  to  the  driving  shaft 
so  that  the  two  revolve  at  the  same  speed. 
For  the  reverse  (Fig.  188,  (5))  an  eighth 
gear  is  thrown  up  from  beneath  so  as 
simultaneously  to  engage  5  and  7.  Such 
an  interposition  of  a  third  gear  wheel 
between  5  and  7  obviously  reverses  the 
direction  of  rotation  of  the  driving  shaft. 
244.  The  differential.  An  automobile 
is  driven  by  .power  applied  to  the  rear 
axle.  This  requires  the  axle  to  be  in  two 

parts  with  a  differential  between,  so  that  in  turning  corners  the  outer 
wheel  may  revolve  faster  than  the  inner.  It  will  be  seen  from  the 
large  drawing  opposite  page  198,  and  from  Fig.  189,  that  the  pinion 


FIG.  189.    The  differential 


198  CHANGE  OF  STATE 

attached  to  the  driving  shaft  rotates  the  main  bevel  gear  B,  to  which 
are  rigidly  attached  the  differential  gears  1  and  2.  The  left  axle  is 
directly  connected  to  gear  3,  and  only  indirectly  connected  to  the  main 
bevel  gear  B  through  gears  1  and  2.  In  running  straight  both  rear 
wheels  revolve  at  the  same  rate;  therefore,  while  gears  3  and  4  and 
the  main  bevel  gear  are  revolving  at  the  same  speed  they  carry  around 
with  them  pinions  1  and  2,  which  are  now,  however,  not  revolving  on 
their  bearings.  When  the  car  is  turning  a  corner,  gears  3  and  4  are 
turning  at  different  rates ;  hence  pinions  1  and  2  are  not  only  carried 
around  by  the  main  bevel  gear  but  at  the  same  time  are  revolved  in 
opposite  directions  on  their  bearings. 

245.  The   carburetor.     The   carburetor   is  a    device   for  converting 
liquid  gasoline,  kerosene,  etc.  into  -vapor  and  mixing  it  with  air  in 
proper  proportions  for  complete  combustion.    ,The  simple  principle  of 
carburetion  is  shown  in  the  upper  diagram  opposite  page  199.    Liquid 
gasoline  comes  through  the  supply  pipe  and  enters  the  float  chamber 
through  the  valve  V.   By  acting  on  the  levers  L  the  float  closes  the  valve 
V  when  the  gasoline  reaches  a  certain  level.   From  the  float  chamber 
the  gasoline  is  drawn  to  the  spray  nozzle  O.  While  the  engine  is  running, 
the  downward  movement  of  the  pistons  in  stroke  1  (Fig.  187)  sucks 
air  violently  past  the  spray  nozzle  into  the  region  called  the  venturi, 
where  the  jet  of  gasoline  is  emerging  from  0.    The  spray  of  fuel  thus 
formed  intermingles  with  air  in  the  mixing  chamber  and  passes  by  the 
throttle  to  the  engine  as  a  highly  explosive  mixture. 

246.  The  ignition.    The  lower  diagram  opposite  page  199  illustrates 
the  principle  of  high-tension  magneto  ignition  which  is  widely  used  on 
automobiles.    A  rolling  contact  R  is  mounted  on  the  cam  shaft,  which 
revolves  at  half  crank-shaft  speed  and  is  carried  around  the  interior  of 
the  stationary  fiber  ring  D.   When  the  switch  S  is  closed  and  the  roller 
R  passes  across  the  metal  segment  G,  a  current  of  electricity  passes  from 
the  magneto  through  the  rolling  contact  to  the  central  shaft  C,  and  from 
there  through  the  iron  work  of  the  car  to  the  magneto  by  way  of  the 
primary  coil  of  the  induction  coil.    While  the  roller  is  in  contact  with 
the  segment  G  the  induction  coil  produces  a  shower  of  sparks  between 
the  points  P  of  the  spark  plug,  thus  igniting  the  explosive  mixture 
in  the  cylinder  of  the  engine.    Since  the  power  stroke  of  the  piston 
occurs  but  once  in  two  revolutions  of  the  crank  shaft,  it  is  necessary 
that  the  crank  shaft  revolve  twice  while  the  contact  revolves  but  once. 
This,  as  shown  in  the  diagram,  is  accomplished  by  having  the  crank 
shaft  geared  to  the  cam  shaft  in  a  velocity  ratio  of  2  to  1. 


To  Engine 


Throttle 
-Mixing  chamber 

Venturi 
-Spray  nozzle 


Needle  valve 


Gasoline  supply 


THE  C A  11  B u RBTO R 


Insulating 
Fibre  Ring 


Magneto 

ro0s"i 

/    .    \ 

SmtchAS 


Cam  Sraft  Gear 
(42  Teeth) 


Lever  Jor  moving  ring  D 
-Metal  Segment 
Rolling  Contact 


^-Crank  Shaft  Gear 
3       (ZITeeth) 


'rank  Handle 


Ax  IGNITION  SYSTEM 


INDUSTRIAL  APPLICATIONS 


199 


The  explosive  mixture  requires  a  very  short  but  measurable  time  for 
combustion ;  hence  the  full  force  of  the  explosion  occurs  a  short  time 
after  the  spark  ignites  the  mixture.  Therefore,  at  high  speed  the  spark 
should  occur  a  little  earlier  with  reference  to  the  position  of  the  piston 
than  at  low  speed.  The  spark  is  advanced  or  retarded  by  a  spark  lever 
L  which  changes  the  position  of  the  segment  G  by  pulling  around 
slightly  the  movable  fiber  ring  to  which  it  is  attached. 

The  diagram  applies  to  a  one-cylinder  engine.    In  case  the  engine  has 
four  cylinders,  three  additional  segments  must  be  added,  as  indicated 
by   the  clear  spaces,   together 
with  three  additional  induction 
coils  and  spark  plugs.* 

247.  The  steam  turbine.  The  r 

steam   turbine    represents   the  M:W 

latest  development  of  the  heat 
engine.  In  principle  it  is  very 
much  like  the  common  wind- 
mill, the  chief  difference  being 
that  it  is  steam  instead  of  air 
which  is  driven  at  a  high  veloc- 
ity against  a  series  of  blades 
arranged  radially  about  the  cir- 
cumference of  the  wheel  that 
is  set  into  rotation.  The  steam, 
however,  unlike  the  wind,  is  FlG  190<  The  principle  of  the 

always  directed  by  nozzles  at  steam  turbine 

the  angle  of  greatest  efficiency 

against  the  blades  (see  Fig.  190).  Furthermore,  since  the  energy  of  the 
steam  is  far  from  spent  after  it  has  passed  through  one  set  of  blades 
(such  as  that  shown  in  Fig.  190),  it  is  in  practice  always  passed  through 
a  whole  series  of  such  sets  (Fig.  191),  every  alternate  row  of  which  is 
rigidly  attached  to  the  rotating  shaft,  while  the  intermediate  rows  are 
fastened  to  the  immovable  outer  jacket  of  the  engine  and  only  serve  as 
guides  to  redirect  the  steam  at  the  most  favorable  angle  against  the 
next  row  of  movable  blades.  In  this  way  the  steam  is  kept  alternately 
bounding  from  fixed  to  movable  blades  until  its  energy  is  expended.  The 
number  of  rows  of  blades  is  often  as  high  as  sixteen. 

*  The  pupil  may  well  consult  the  more  extended  treatises  for  actual  details 
of  the  many  different  systems  of  ignition  used  on  automobile  and  airplane 
engines. 


200 


CHANGE  OF  STATE 


Turbines  are  at  present  coming  rapidly  into  use,  chiefly  for  large- 
power  purposes.  Their  advantages  over  the  reciprocating  steam  engine 
lie  first  in  the  fact  that  they  run  with  almost  no  jarring,  and  therefore 
require  much  lighter  and  less  expensive  foundations,  and  second  in  the 
fact  that  they  occupy  less  than  one  tenth  the  floor  space  of  ordinary 
engines  of  the  same  capacity.  Their  efficiency  is  fully  as  high  as  that 

Exhaust 


Revolving 


Stationary 


Revolving 


Nozzle 


FIG.  191.    Path  of  steam  in  Curtis's  turbine 


of  the  best  reciprocating  engines.  The  highest  speeds  attained  by  ves- 
sels at  sea,  namely,  about  40  miles  per  hour,  have  been  made  with  the 
aid  of  steam  turbines.  One  of  the  largest  vessels  which  have  thus  far 
been  launched,  the  Berengaria,  919  feet  long,  98  feet  wide,  100  feet  high 
(from  the  keel  to  the  top  of  her  ninth  deck),  having  a  total  displace- 
ment of  57,000  tons  and  a  speed  of  221  knots,  is  driven  by  four  steam 
turbines  having  a  total  horse  power  of  61,000.  One  of  the  immense 
rotors  contains  50,000  blades  and  develops  22,000  horse  power.  The 
United  States  Shipping  Board,  on  July  24,  1919,  announced  plans  for 


INDUSTRIAL  APPLICATIONS 


201 


building  two  gigantic  ocean  liners  swifter  and  larger  than  any  afloat. 
They  are  to  be  1000  feet  long  and  are  to  have  a  horse  power  of  110,000 
and  a  speed  of  30  knots.  (See  opposite  p.  135.) 

248.  Manufactured  ice.  In  the  great  majority  of  modern  ice  plants 
the  low  temperature  required  for  the  manufacture  of  the  ice  is  produced 
by  the  rapid  evaporation  of  liquid  ammonia.  At  ordinary  temperatures 
ammonia  is  a  gas,  but  it  may  be  liquefied  by  pressure  alone.  At  80°  F. 
a  pressure  of  155  pounds  per  square  inch,  or  about  10  atmospheres,  is 
required  to  produce  its  liquefaction.  Fig.  192  shows  the  essential  parts 
of  an  ice  plant.  The  compressor,  which  is  usually  run  by  a  steam  engine, 


Low  Pressure 
Gau 


HighPressure 
Gauge 


FIG.  192.    Compression  system  of  ice  manufacture 


forces  the  gaseous  ammonia  under  a  pressure  of  155  pounds  into  the  con- 
denser coils  shown  on  the  right,  and  there  liquefies  it.  The  heat  of  con- 
densation of  the  ammonia  is  carried  off  by  the  running  water  which 
constantly  circulates  about  the  condenser  coils.  From  the  condenser 
the  liquid  ammonia  is  allowed  to  pass  very  slowly  through  the  regulat- 
ing valve  V  into  the  coils  of  the  evaporator,  from  which  the  evaporated 
ammonia  is  pumped  out  so  rapidly  that  the  pressure  within  the  coils 
does  not  rise  above  34  pounds.  It  will  be  noted  from  the  figure  that 
the  same  pump  which  is  there  labeled  the  compressor  exhausts  the 
ammonia  from  the  evaporating  coils  and  compresses  it  in  the  condensing 
coils,  for  the  valves  are  so  arranged  that  the  pump  acts  as  an  exhaust 
pump  on  one  side  and  as  a  compression  pump  on  the  other.  The  rapid 
evaporation  of  the  liquid  ammonia  under  the  reduced  pressure  existing 


202  CHANGE  OF  STATE 

within  the  evaporator  cools  these  coils  to  a  temperature  of  about  5°  F. 
The  brine  with  which  these  coils  are  surrounded  has  its  temperature 
thus  reduced  to  about  16°  or  18°  F.  This  brine  is  made  to  circulate 
about  the  cans  containing  the  water  to  be  frozen.  The  heat  of  vapori- 
zation of  ammonia  at  5°  F.  is  314  calories. 

Many  thousands  of  feet  of  circulating  saltwater  pipe  are  laid  horizon- 
tally and  covered  with  water  to  be  frozen  for  large  indoor  skating  rinks. 

249.  Cold  storage.  The  artificial  cooling  of  factories  and  cold-storage 
rooms  is  accomplished  in  a  manner  exactly  similar  to  that  employed 
in  the  manufacture  of  ice.  The  brine  is  cooled  precisely  as  described 
above,  and  is  then  pumped  through  coils  placed  in  the  rooms  to  be 
cooled.  In  some  systems  carbon  dioxide  is  used  instead  of  ammonia, 
but  the  principle  is  in  no  way  altered.  Sometimes,  too,  the  brine  is 
dispensed  with,  and  the  air  of  the  rooms  to  be  cooled  is  forced  by  means 
of  fans  directly  over  the  cold  coils  containing  the  evaporating  ammonia 
or  carbon  dioxide.  It  is  in  this  way  that  theaters  and  hotels  are  cooled. 

QUESTIONS  AND  PROBLEMS 

1.  Why  is  a  gas  engine  called  an  internal-combustion  engine  ? 

2.  Why  do  gasoline  engines  have  flywheels  ?   Why  is  a  one-cylinder 
engine  of  the  four-cycle  type  especially  in  need  of  a  flywheel  ? 

3.  How  does  the  temperature  of  the  steam  within  a  locomotive  boiler 
compare  with  its  temperature  at  the  moment  of  exhaust  ?  Explain. 

4.  On  the  drive  wheels  of  locomotives  there  is  a  mass  of  iron  op- 
posite the  point  of  attachment  of  the  drive  shaft.   Why  is  this  necessary  ? 

5.  Why  does  not  the  water  in  a  locomotive  boil  at  100°  C.  ? 

6.  If  liquid  oxygen  is  placed  in  an  open  vessel,  its  temperature  will 
not  rise  above  — 182°  C.    Why  not?    Suggest  a  way  in  which  its  tem- 
perature could  be  made  to  rise  above  — 182°  C.,  and  a  way  in  which  it 
could  be  made  to  fall  below  that  temperature. 

7.  How  many  foot  pounds  of  energy  are  there  in  1  Ib.  of  coal  con- 
taining 14,000  B.  T.  U.  per  pound  ?   How  many  pounds  of  iron  must  be 
held  at  a  height  of  150  ft.  to  have  as  much  energy  as  this  pound  of  coal? 

8.  The  average  locomotive  has  an  efficiency  of  abdut  6%.    What 
horse  power  does  it  develop  when  it  is  consuming  1  ton  of  coal  per 
hour?    (See  Problem  7,  above.) 

9.  What  amount  of  useful  work  did  a  gasoline  engine  working  at 
an  efficiency  of  25%  do  in  using  100  Ib.  of  gasoline  containing  18,000 
B.T.U.  per  pound? 

10.  What  pull  does  a  1000  H.P.  locomotive  exert  when  it  is  running 
at  25  mi.  per  hour  and  exerting  its  full  horse  power? 


CHAPTER  XI 


THE  TRANSFERENCE  OF  HEAT 

CONDUCTION 

250.  Conduction  in  solids.  If  one  end  of  a  short  metal  bar  is 
held  in  the  fire,  the  other  end  soon  becomes  too  hot  to  hold ;  but  if  the 
metal  rod  is  replaced  by  one  of  wood  or  glass,  the  end  away  from  the 
flame  is  not  appreciably  heated. 

This  experiment  and  others  like  it  show  that  nonmetallic 
substances  possess  much  less  ability  to  conduct  heat  than 
do  metallic  substances.  But  although 
all  metals  are  good  conductors  as 
compared  with  nonmetals,  they  differ 
widely  among  themselves  in  their  con- 
ducting powers. 

Let  copper,  iron,  and  German-silver  wires 
50  cm.  long  and  about  3  mm.  in  diameter  be 
twisted  together  at  one  end  as  in  Fig.  193, 
and  let  a  Bunsen  flame  be  applied  to  the 
twisted  ends.  Let  a  match  be  slid  slowly 
from  the  cool  end  of  each  wire  toward  the 

hot  end,  until  the  heat  from  the  wire  ignites  it.    The  .copper  will  be 
found  to  be  the  best  conductor  and  the  German  silver  the  poorest. 

In  the  following  table  some  common  substances  are  arranged 
in  the  order  of  their  heat  conductivities.  The  measurements 
have  been  made  by  a  method  not  differing  in  principle  from 
that  just  described.  For  convenience,  silver  is  taken  as  100. 


FIG.  193.    Differences  in 

the  heat  conductivities  of 

metals 


Silver  .     .     . 

.     100 

Tin     . 

. 

15 

Mercury  . 

1.5 

Copper     .     . 
Aluminium  . 

74 

.       48 

Iron    . 
Lead  . 

.     .     . 

12 

8.5 

Ice      .... 

Glass  .... 

.21 
.15 

Brass  . 

.       27 

German 

silver  . 

6.3 

Hard  rubber     . 

.04 

203 

204 


THE  TRANSFERENCE  OF  HEAT 


FIG.  194.    Water  a  nonconductor 


251.  Conduction  in  liquids  and  gases.    Let  a  small  piece  of  ice 
be  held  by  means  of  a  glass  rod  in  the  bottom  of  a  test  tube  full  of  ice 
water.     Let  the  upper  part  of  the 

tube  be  heated  with  a  Bunsen 
burner  as  in  Fig.  194.  The  upper 
part  of  the  water  may  be  boiled  for 
some  time  without  melting  the  ice. 
Water  is  evidently,  then,  a  very  poor 
conductor  of  heat.  The  same  thing 
may  be  shown  more  strikingly  as 
follows :  The  bulb  of  an  air  ther- 
mometer is  placed  only  a  few  milli- 
meters beneath  the  surface  of  water 
contained  in  a  large  funnel  arranged 
as  in  Fig.  195.  If  now  a  spoonful 

of  ether  is  poured  on  the  water  and  set  on  fire,  the  index  of  the  air 
thermometer  will  show  scarcely  any  change,  in  spite  of  the  fact  that 
the  air  thermometer  is  a  very  sensitive  indicator  of 
changes  in  temperature. 

Careful  measurements  of  the  conductivity 
of  water  show  that  it  is  only  about  121QO  of 
that  of  silver.  The  conductivity  of  gases  is 
even  less,  not  amounting  on  the  average  to 
more  than  ^  that  of  water. 

252.  Conductivity  and  sensation.    It  is  a 
fact  of  common  observation  that  on  a  cold 
day  in  winter  a  piece  of  metal  feels  much 
colder  to  the  hand   than  a  piece  of  wood, 
notwithstanding  the  fact  that  the  tempera- 
ture of  the  wood  must  be  the  same  as  that 
of  the  metal.    On  the  other  hand,  if  the  same 
two  bodies  had  been  lying  in  the  hot  sun  in 
midsummer,  the  wood  might  be  handled  without  discomfort, 
but  the  metal  would  be  uncomfortably  hot.    The  explanation 
of  these  phenomena  is  found  in  the  fact  that  the  iron,|being 
a  much  better  conductor  than  the  wood,  removes  heaF  from 


FIG.  195.  Burning 
ether  on  the  water 
does  not  affect  the 
air  thermometer 


CONDUCTION  205 

the  hand  much  more  rapidly  in  winter,  and  imparts  heat 
to  the  hand  much  more  rapidly  in  summer,  than  does  the 
wood.  In  general,  the  better  a  conductor  the  hotter  it  will 
feel  to  a  hand  colder  than  itself,  and  the  colder  to  a  hand 
hotter  than  itself.  Thus,  in  a  cold  room  oilcloth,  a  fairly 
good  conductor,  feels  much  colder  to  the  touch  than  a  carpet, 
a  comparatively  poor  conductor.  For  the  same  reason  linen 
clothing  feels  cooler  to  the  touch  in  winter  than  woolen  goods. 

253.  The  role  of  air  in  nonconductors.    Feathers,  fur,  felt, 
etc.  make  very  warm  coverings,  because  they  are  very  poor 
conductors  of  heat  and  thus  prevent  the  escape  of  heat  from 
the  body.    Their  poor  conductivity  is  due  in  large  measure  to 
the  fact  that  they  are  full  of  minute  spaces  containing  air, 
and  gases  are  the  best  nonconductors  of  heat.    It  is  for  this 
reason  that  freshly  fallen  snow  is  such  an  efficient  prqtection 
to  vegetation.    Farmers  always  fear  for  their  fruit  trees  and 
vines  when  there  is  a  severe  cold  snap  in  winter,  unless  there 
is  a  coating  of  snow  on  the  ground  to  prevent  a  deep  freezing. 

254.  The  Davy  safety  lamp.    Let  a  piece  of  wire  gauze  be  held 
above  an  open  gas  jet  and  a  match  applied  above  the  gauze.    The  flame 
will  be  found  to  burn  above  the  gauze 

as  in  Fig.  196,  (1),  but  it  will  not 
pass  through  to  the  lower  side.  If 
it  is  ignited  below  the  gauze,  the 
flame  will  not  pass  through  to  the 
upper  side  but  will  burn  as  shown 
in  Fig.  196,  (2). 

The  explanation  is  found  in 
,  T       r>         ,T         ,i  T  FIG.  196.   A  flame  will  not  pass 

the  fact  that  the  gauze  conducts  through  wire  gauze 

the  heat  away  from  the  flame  so 

rapidly  that  the  gas  on  the  other  side  is  not  raised  to  the 
temperature  of  ignition.  Safety  lamps  used  by  miners  are 
completely  incased  in  gauze,  so  that  if  the  mine  is  full  of 
inflammable  gases,  they  are  not  ignited  outside  of  the  gauze 
by  the  lamp. 


206 


THE  TKANSFERENCE  OF  HEAT 


FIG.  197.   A  lireless  cooker 


QUESTIONS  AND  PROBLEMS 

1.  With  the  aid  of  Fig.  197,  which  represents  a  fireless  cooker,  ex- 
plain the   principle  on  which  fireless,  cooking  is  done. 

2.  Why  do  firemen  wear  flannel  shirts  in  summer  to  keep  cool  and 
in  winter  to  keep  warm  ? 

3.  If  a  package  of  ice  cream  is 
put  inside  a  paper  bag,  it  will  not 
melt  so  fast  on  a  hot  day.    Explain. 

4.  If  the  ice  in  a  refrigerator  is 
wrapped  up  in  blankets,  what  is  the 
effect  on  the  ice  ?  on  the  refrigerator  ? 

5.  If  a  piece  of  paper  is  wrapped 
tightly  around  a  metal  rod  and  held 
for  an  instant  in  a  Bunsen  flame,  it 
will  not  be  scorched.    If  held  in  a 
flame  when  wrapped  around  a  wooden 
rod,    it    will    be    scorched    at    once. 
Explain. 

6.  If  one  touches  the  pan  contain- 
ing a  loaf  of  bread  in  a  hot  oven,  he  receives  a  much  more  severe  burn 
than  if  he  touches  the  bread  itself,  although  the  two  are  at  the  same 
temperature.    Explain. 

7.  Why  are  plants  often  covered  with  paper  on  a  night  when  frost 
is  expected? 

8.  Why  will  a  moistened  finger  or  the  tongue  freeze  instantly  to  a 
piece  of  iron  on  a  cold  winter's  day,  but  not  to  a  piece  of  wood  ? 

9.  Does  clothing  ever  afford  us  heat  in  winter?   How,  then,  does  it 
keep  us  warm  ? 

10.  Why  is  the  outer  pail  of  an  ice-cream  freezer  made  of  thick  wood 
and  the  inner  can  of  thin  metal  ? 

CONVECTION 

255.  Convection  in  liquids.  Although  the  conducting  power 
of  liquids  is  so  small,  as  was  shown  in  the  experiment  of  §  251, 
they  are  yet  able,  under  certain  circumstances,  to  transmit 
heat  much  more  effectively  than  solids.  Thus,  if  the  ice  in  the 
experiment  of  Fig.  194  had  been  placed  at  the  top  and  the 
flame  at  the  bottom,  the  ice  would  have  been  melted  very 
quickly.  This  shows  that  heat  is  transferred  very  much 


CONVECTION 


207 


more  readily  from  the  bottom  of  the  tube  toward  the  top 
than  from  the  top  toward  the  bottom.  The  mechanism  of 
this  heat  transference  will  be  evident  from  the  following 
experiment : 

Let  a  round-bottomed  flask  (Fig.  198)  be  half  filled  with  water  and 
a  few  crystals  of  magenta  dropped  into  it.  Then  let  the  bottom  of  the 
flask  be  heated  with  a  Bunsen  burner.  The  magenta 
will  reveal  the  fact  that  the  heat  sets  up  currents 
the  direction  of  which  is  upward  in  the  region  im- 
mediately above  the  flame  but  downward  at  the  sides 
of  the  vessel.  It  will  not  be  long  before  the  whole 
of  the  water  is  uniformly  colored.  This  shows  how 
thorough  is  the  mixing  accomplished  by  the  heating. 

The  explanation  of  the  phenomenon  is  as 
follows:  The  water  nearest  the  flame  be- 
came heated  and  expanded.  It  was  thus  ren- 
dered less  dense  than  the  surrounding  water, 
and  was  accordingly  forced  to  the  top  by 
the  pressure  transmitted  from  the  colder 
and  therefore  denser  water  at  the  sides 
which  then  came  in  to  take  its  place. 

It  is  obvious  that  this  method  of  heat  transfer' is  applicable 
only  to  fluids.  The  essential  difference  between  it  and  con- 
duction is  that  the  heat  is  not  transferred  from  molecule  to 
molecule  throughout  the  whole  mass,  but  is  rather  transferred 
by  the  bodily  movement  of  comparatively  large  masses  of 
the  heated  liquid  from  one  point  to  another.  This  method 
of  heat  transference  is  known  as  convection. 

256.  Winds  and  ocean  currents.  Winds  are  convection  cur- 
rents in  the  atmosphere  caused  by  unequal  heating  of  the 
earth  by  the  sun.  Let  us  consider,  for  example,  the  land  and 
sea  breezes  so  familiar  to  all  dwellers  near  the  coasts  of  large 
bodies  of  water.  During  the  daytime  the  land  is  heated  more 
rapidly  than  the  sea,  because  the  specific  heat  of  water  is 
much  greater  than  that  of  earth.  Hence  the  hot  air  over  the 


FIG.  198.    Convec- 
tion currents 


208  THE  TRANSFERENCE  OF  HEAT 

land  expands  and  is  forced  up  by  the  colder  and  denser  air 
over  the  sea  which  moves  in  to  take  its  place.  This  con- 
stitutes the  sea  breeze,  which  blows  during  the  daytime, 
usually  reaching  its  maximum  strength  in  the  late  afternoon. 
At  night  the  earth  cools  more  rapidly  than  the  sea  and  hence 
the  direction  of  the  wind  is  reversed.  The  effect  of  these 
breezes  is  seldom  felt  more  than  twenty-five  miles  from  shore. 
Ocean  currents  are  caused  partly  by  the  unequal  heating 
of  the  sea  and  partly  by  the  direction  of  the  prevailing 
winds.  In  general,  both  winds  and  currents  are  so  modified 
by  the  configuration  of  the  continents  that  it  is  only  over 
broad  expanses  of  the  ocean  that  the  direction  of  either  can 
be  predicted  from  simple  considerations. 

RADIATION 

257.  A  third  method  of  heat  transference.  There  are  certain 
phenomena  in  connection  with  the  transfer  of  heat  for  which 
conduction  and  convection  are  wholly  unable  to  account, 
For  example,  if  one  sits  in  front  of  a  hot  grate  fire,  the 
heat  which  he  feels  cannot  come  from  the  fire  by  convection, 
because  the  Currents  of  air  are  moving  toward  the  fire  rather 
than  away  from  it.  It  cannot  be  due  to  conduction,  because 
the  conductivity  of  ah-  is  extremely  small  and  the  colder 
currents  of  air  moving  toward  the  fire  would  more  than 
neutralize  any  transfer  outward  due  to  conduction.  There 
must  therefore  be  some  way  in  which  heat  travels  across  the 
intervening  space  other  than  by  conduction  or  convection. 

It  is  still  more  evident  that  there  must  be  a  third  method 
of  heat  transfer  when  we  consider  the  heat  which  comes  to 
us  from  the  sun.  Conduction  and  convection  take  place  only 
through  the  agency  of  matter;  but  we  know  that  the  space 
between  the  earth  and  the  sun  is  not  filled  with  ordinary 
matter,  or  else  the  earth  would  be  retarded  .  in  its  motion 
through  space.  Radiation  is  the  name  given  to  this  third 


RADIATION  209 

method  by  which  heat  travels  from  one  place  to  another, 
and  which  is  illustrated  in  the  passing  of  heat  from  a  grate 
fire  to  a  body  in  front  of  it,  or  from  the  sun  to  the  earth. 

258.  The  nature  of  radiation.    The  nature  of  radiation  will 
be  discussed  more  fully  in  Chapter  XXI.   It  will  be  sufficient 
here  to  call  attention  to  the  following  differences  between 
conduction,  convection,  and  radiation. 

First,  while  conduction  and  convection  are  comparatively 
slow  processes,  the  transfer  of  heat  by  radiation  takes  place 
with  the  enormous  speed  with  which  light  travels,  namely 
186,000  miles  per  second.  That  the  two  speeds  are  the  same 
is  evident  from  the  fact  that  at  the  time  of  an  eclipse  of  the 
sun  the  shutting  off  of  heat  from  the  earth  is  observed  to  take 
place  at  the  same  time  as  the  shutting  off  of  light. 

Second,  radiant  heat  travels  in  straight  lines,  while  conducted 
or  convected  heat  may  follow  the  most  circuitous  routes.  The 
proof  of  this  statement  is  found  in  the  familiar  fact  that  ra- 
diation may  be  cut  off  by  means  of  a  screen  placed  directly 
between  a  source  and  the  body  to  be  protected. 

Third,  radiant  heat  may  pass  through  a  medium  without 
heating  it.  This  is  shown  by  the  fact  that  the  upper  regions 
of  the  atmosphere  are  very  cold,  even  in  the  hottest  days  in 
summer,  or  that  a  hothouse  may  be  much  warmer  than  the 
glass  through  which  the  sun's  rays  enter  it. 

259.  The   Dewar  flask  and  the  thermos  bottle.    For  the 
retention   of  extremely  cold  liquids,   such,  for  example,    as 
liquefied  air,  whose  boiling  point  is  -190°  C.  (=-  310°  F.), 
Dewar  invented  a  double-walled  vessel.    The  space  between 
the  walls  is  a. vacuum,  and  the  inner  surface  of  the  outer 
vessel  and  the  outer  surface  of  the  inner  vessel  are  silvered. 
There  are  three  ways  in  which  heat  may  pass  inward  through 
the  double  wall  —  conduction,  convection,  and  radiation.  The 
vacuum  prevents  almost  entirely  the  first  two,  while  the  silver- 
ing eliminates  passage  of  heat  by  radiation.    The  well-known 


210 


THE  TRANSFERENCE  OF  HEAT 


glass  part  of  the  thermos  bottle  (Fig.  199)  is  simply  a 
cylindrical  Dewar  flask  for  keeping  liquids  either  hot  or 
cold,  since  it  is  as  difficult  for  heat  to  pass  outward  through 
the  walls  as  to  pass  inward.  The  glass  flask  is  provided  with 
a  cork  stopper,  and  a  strong  outside  metal 
case  for  its  protection.  Hot  liquids,  as  well  as  /) 

those  that  are  cold,  may  be  kept  for  several 
hours  in  a  thermos  bottle  with  only  a  few 
degrees  change  in  temperature. 

THE  HEATING  AND  VENTILATING  OF 
BUILDINGS 


260.  The  principle  of  ventilation.  The  heating 
and  ventilating  of  buildings  are  accomplished 
chiefly  through  the  agency  of  convection. 


FIG.  199.  The  in- 
ner glass  flask  of 
a  thermos  bottle 


To  illustrate  the  principle  of  ventilation  let  a  candle  be  lighted  and 
placed  in  a  vessel  containing  a  layer  of  water  (Fig.  200).   When  a  lamp 
chimney  is  placed  over  the  candle  so  that  the 
bottom  of  the  chimney  is  under  the  water,  the 
flame  will  slowly  die  down  and  will  finally 
be  extinguished.    This  is  because  the  oxygen, 
which  is  essential  to  combustion,  is  gradually  used  up 
and  no  fresh  supply  is  possible  with  the  arrangement 
described.    If  the  chimney  is  raised  even  a  very  little 
above  the  water,  the  dying  flame  will  at  once  brighten. 
Why?  If  a  metal  or  cardboard. partition  is  inserted  in 
the  chimney,  as  in  Fig.  200,  the  flame  will  burn  con- 
tinuously, even  when  the  bottom  of  the  chimney  is 
under  water.    The  reason  will  be  clear  if  a  piece  of 
burning  touch  paper  (blotting  paper  soaked  in  a  solu- 
tion of  potassium  nitrate  and  dried)  is  held  over  the 
chimney.    The  smoke  will  show  the  direction  of  the 
air  currents.    If  the  chimney  is  a  large  one,  in  order 
that  the  first  part  of  the  above  experiment  may  succeed, 
it  may  be  necessary  to  use  two  candles ;  for  too  small 
a  heated  area  permits  the  formation  of  downward  currents  at  the  sides. 


FIG.  200.     Con- 
vection currents 
in  air 


HEATING  AND  VENTILATING 


211 


261.  Ventilation  of  houses.    In  order  to  secure  satisfactory 
ventilation  it  is  estimated  that  a  room  should  be  supplied  with 

2000  cubic  feet  of  fresh  air  per  hour  for  each  occupant 
(a  gas  burner  is  equivalent  in  oxygen  consumption  to 

four  persons).  A 
current  of  air  mov- 
ing with  a  speed 
great  enough  to  be 
just  perceptible  has 
a  velocity  of  about 
3  feet  per  second. 
Hence  the  area  of 
opening  required  for 
each  person  when 
fresh  air  is  entering 
at  this  speed  is 
about  25  or  30 
square  inches.  The 
manner  of  supply- 
ing this  requisite 

amount  of  fresh  air  in  dwelling  houses   depends  upon  the 

particular  method  of  heating  employed. 
If  a  house  is  heated  by  stoves  or  fireplaces, 

no  special  provision  for  ventilation  is  needed. 

The  foul  air  is  drawn  up  the  chimney  with 

the  smoke,  and  the  fresh  air  which  replaces 

it   finds   entrance   through   cracks    about   the 

doors  and  windows  and   through  the  walls. 

262.  Hot-air  heating.    In  houses  heated  by  hot-air 
furnaces  an  air  duct  ought  always  to  be  supplied  for 
the  entrance  of  fresh  cold  air,  in  the  manner  shown 
in  Fig.  201  (see  "  cold-air  inlet  ").    This  cold  air  from 

out  of  doors  is  heated  by  passing  in  a  circuitous  way,  FIG. 202.  Princi- 
as  shown  by  the  arrows,  over  the  outer  jacket  of  iron  p]e  of  hot-water 
which  covers  the  fire  box.  It  is  then  delivered  to  the  heating 


FIG.  201.    Ho^-air  heating 


212 


THE  TRANSFERENCE  OF  HEAT 


rooms.  Here  a  part  of  it  escapes  through  windows  and  doors,  and  the 
rest  returns  through  the  cold-air  register  to  be  reheated,  after  being 
mixed  with  a  fresh  supply  from  out  of  doors. 

When  the  fire  is  first  started,  in  order  to  gain  a  strong  draft  the 
damper  C  is  opened  so  that  the  smoke 
may    pass    directly    up     the    chimney. 
After  the  fire  is  under  way  the  damper 
C  is  closed  so  that  the  smoke  and  hot 


Cold  water 


Copper 

heating 

coils 


FIG.  203.   A  gas  heating  coil 


FIG.  204.    Hot-water  heater 


gases  from  the  furnace  must  pass,  as  indicated  by  the  dotted  arrows, 
over  a  roundabout  path,  in  the  course  of  which  they  give  up  the  major 
part  of  their  heat  to  the  steel  walls  of  the  jacket,  which  in  turn  pass 
it  on  to  the  air  which  is  on  its  way  to  the-  living  rooms. 

263.  Hot-water  heating.  To  illustrate  the  principle  of  hot-water 
heating  let  the  arrangement  shown  in  Fig.  202  be  set  up,  the  upper 
vessel  being  filled  with  colored  water,  and  then  let  a  flame  be  applied 
to  the  lower  vessel.  The  colored  water  will  show  that  the  current  moves 
in  the  direction  of  the  arrows. 


HEATING  AND  VENTILATING  213 

This  same  principle  is  involved  in  the  gas  heating  coil  used  in 
connection  with  the  kitchen  boiler  (Fig.  203).  Heat  from  the  flame 
passes  through  the  copper  coil  to  the  water,  and  convection  begins  as 
indicated  by  the  arrows.  When  hot  water  is  drawn  from  the  top  of  the 
boiler,  cold  water  enters  near  the  bottom  so  as  not  to  mingle  with  the 
hot  water  that  is  being  used.  The  principle  is  still  further  illustrated 
by  the  cooling  systems  used  for  keeping  automobile  engines  from 
becoming  overheated.  Heat  passes  from  the  engine  into  the  water, 
which  loses  heat  in  circulating  through  the  coils  of  the  radiator. 

The  actual  arrangement  of  boiler  and  radiators  in  one  system  of  hot- 
water  heating  is  shown  in  Fig.  204.  The  water  heated  in  the  furnace 
rises  directly  through  the  pipe  A  to  a  radiator  R,  and  returns  again  to 
the  bottom  of  the  furnace  through  the  pipes  B  and  D.  The  circulation 
is  maintained  because  the  column  of  water  in  A  is  hotter  and  therefore 
lighter  than  the  water  in  the  return  pipe  B. 

By  eliminating  the  expansion  tank  and  partly  filling  the  boiler  with 
water  the  system  could  be  converted  into  a  steam-heating  plant. 

QUESTIONS  AND  PROBLEMS 

1.  If  we  attempt  to  start  a  fire  in  the  kitchen  range  when  the  chimney 
is  cold  and  damp,  the  range  "  smokes."    Explain. 

2.  Why  is  a  hollow  wall  filled  with  sawdust  a  better  nonconductor 
of  heat  than  the  same  wall  filled  with  air  alone  ? 

3.  In  a  system  of  hot-water  heating  why  does  the  return  pipe  always 
connect  at  the  bottom  of  the  boiler,  while  the  outgoing  pipe  connects 
with  the  top  ? 

4.  Which  is  thermally  more  efficient,  a  cook  stove  or  a  grate?  Why? 

5.  When  a  room  is  heated  by  a  fireplace,  which  of  the  three  methods 
of  heat  transference  plays  the  most  important  role  ? 

6.  Why  do  you  blow  on  your  hands  to, warm  them  in  winter  and 
fan  yourself  for  coolness  in  summer? 

7.  If  you  open  a  door  between  a  warm  and  a  cold  room,  in  what 
direction  will  a  candle  flame  be  blown  which  is  placed  at  the  top  of  the 
door?   Explain. 

8.  Why  is   felt  a  better  conductor  of  heat  when  it  is  very  firmly 
packed  than  when  loosely  packed? 

9.  If  2  metric  tons  of  coal  are  burned  per  month  in  your  house,  and 
if  your  furnace  allows  one  third  of  the  heat  to  go  up  the  chimney, 
how  many  calories  remain  to  be  used  per  day  ?    (Take  1  g.  as  yielding 
6000  calories.    A  metric  ton  =  1000  kg.) 


CHAPTER  XII 

MAGNETISM* 
GENERAL  PROPERTIES  OF  MAGNETS 

264.  Magnets.  It  has  been  known  for  many  centuries  that 
some  specimens  of  the  ore  known  as  magnetite  (Fe3O4)  have 
the  property  of  attracting  small  bits  of  iron  and  steel.  This 
ore  probably  received  its  name  from  the  fact  that  it  was 
first  observed  in  the  province  of  Magnesia,  in  Thessaly. 
Pieces  of  this  ore  which  exhibit  this  attractive  property  are 
known  as  natural  magnets. 

It  was  also  known  to  the  ancients  that  artificial  magnets 
may  be  made  by  stroking  pieces  of  steel  with  natural  magnets, 
but  it  was  not  until  about  the  twelfth  century  that  the  dis- 
covery was  made  that  ta  suspended  magnet  tvill  assume  a  north- 
and-south  position.  Because  of  this  latter  property  natural 
magnets  became  known  as  lodestones  (leading  stones),  and 
magnets,  either  artificial  or  natural,  began  to  be  used  for  deter- 
mining directions.  The  first  mention  of  the  use  of  the  compass 
in  Europe  is  in  1190.  It  is  thought  to  have  been  introduced 
from  China.  (See  opposite  p.  223  for  the  gyrocompass.) 

Magnets  are  now  made  either  by  stroking  bars  of  steel  in 
one  direction  with  a  magnet,  or  by  passing  electric  currents 
about  the  bars  in  a  manner  to  be  described  later.  The  form 
shown  in  Fig.  205  is  called  a  bar  magnet,  that  shown  in 
Eig.  206  a  horseshoe  magnet.  The  latter  form  is  the  more 
common,  and  is  the  better  form  for  lifting. 

*Tliis  chapter  should  be  either  accompanied  or  preceded  by  laboratory 
experiments  on  magnetic  fields  and  on  the  molecular  nature  ef  magnetism. 
See,  for  example,  Experiments  25  and  26  of  the  authors'  Manual. 

214 


GENERAL  PROPERTIES  OF  MAGNETS 


215 


FIG.  206.    A  horseshoe 
magnet 


If  a  magnet  is  dipped  into  iron  filings,  the  filings  will  be 
seen  to  cling  in  tufts  near  the  ends. but  scarcely  at  all  near 
the  middle  (Fig.  207).  These  places 
near  the  ends  of  a  magnet  at  which  its 
strength  seems  to  be  concentrated  are 
called  the  poles  of  the  magnet.  The  end  of  a  freely  swing- 
ing magnet  which  points  to  the  north  is  designated  as  the 
north-seeking  pole,  or  simply  the  north 
pole  (jV)  ;  and  the  other  end  as  the 
south-seeking  pole,  or  the  south  pole  ($)• 
The  direction  in  ivhich  a  compass  needle 
points  is  called  the  magnetic  meridian. 

265.  The  laws  of  magnetic  attraction  and  repulsion.  In  the 
experiment  with  the  iron  filings  no  particular  difference  was 
observed  between  the  action  of  the 
two  poles.  That  there  is  a  difference, 
however,  may  be  shown  by  experi- 
menting with  two  magnets,  either 
of  which  may  be  suspended  (see 

Fig.  208).  If  two  N  poles  are  brought  near  one  another,  they 
are  found  to  repel  each  other.  The  S  poles  likewise  are  found 
to  repel  each  other.  But  the  N  pole  of 
one  magnet  is  found  to  be  attracted  by  the 
S  pole  of  another.  The  results  of  these 
experiments  may  be  summarized  in  a 
general  law:  Magnet  poles  of  like  kind  repel 
each  other,  while  poles  of  unlike  kind  attract. 

The  force  which  any  two  poles  exert 
upon  each  other  in  air  is  equal  to  the 
product  of  the  pole  strengths  divided  by 

the  square  of  the  distance  between  them.    FlG-  208'   MaSnetic  at- 
,          .          7.-I/.T  17.7       tractions  and  repulsions 

A  unit  pole  is  defined  as  a  pole  which, 

when  placed   at   a   distance   of  1    centimeter  from   an   exactly 
similar  pole,  in  air,  repels  it  with  a  force  of  1   dyne. 


FIG.  207.   Iron  filings  cling- 
ing to  a  bar  magnet 


216 


MAGNETISM 


266.  Magnetic   materials.      Iron   and   steel   are   the   only 
substances  which  exhibit  magnetic  properties  to  any  marked 
degree.    Nickel  and  cobalt  are  also  attracted  appreciably  by 
strong  magnets.    Bismuth,  antimony,  and  a  number  of  other 
substances  are  actually  repelled  instead  of  attracted,  but  the 
effect  is  very  small.    It  has  recently  been  found  possible  to 
make  quite  strongly  magnetic  alloys  out  of  certain  nonmag- 
netic materials.    For  example,  a  mixture  of  65%  copper,  27% 
manganese,   and  8%  aluminium  is  quite  strongly  magnetic. 
These  are  called  Heusler  alloys.  For  practical  purposes,  how- 
ever, iron  and  steel  may  be  considered  as 

the  only  magnetic  materials. 

267.  Magnetic  induction.    If  a  small  un- 
magnetized  nail  is  suspended  from  one  end 
of  a  bar  magnet,  it  is  found  that  a  second 
nail  may  be  suspended  from  this  first  nail, 
which  itself  acts  like  a  magnet,  a  third  from 
the  second,  etc.,  as  shown  in  Fig.  209.   But 
if  the  bar  magnet  is  carefully  pulled  away 

from  the  first  nail,  the  others  will  instantly  fall  away  from 
each  other,  thus  showing  that  the  nails  were  strong  magnets 
only  so  long  as  they  were  in  contact  with  the 
bar  magnet.  Any  piece  of  soft  iron  may 
be  thus  magnetized  temporarily  by  holding 
it  in  contact  with  a  permanent  magnet.  In- 
deed, it  is  not  necessary  that  there  be  actual 
contact,  for  if  a  nail  is  simply  brought  near 
to  the  permanent  magnet  it  is  found  to 
become  a  magnet.  This  may  be  proved  by 
presenting  some  iron  filings  to  one  end  of 
a  nail  held  near  a  magnet  in  the  manner 
shown  in  Fig.  210.  Even  inserting  a  plate  of  glass,  or  of 
copper,  or  of  any  other  material  except  iron  between  S  and  N 
will  not  change  appreciably  the  number  of  filings  which  cling 


FIG.  209.  Magnetism 
induced  by  contact 


FIG.  210.   Magnet- 
ism induced  with- 
out contact 


GENERAL  PROPERTIES  OF  MAGNETS     217 

to  the  end  of  $',  —  a  fact  which  shows  that  nonmagnetic  mate- 
rials are  transparent  to  magnetic  forces.  But  as  soon  as  the 
permanent  magnet  is  removed,  most  of  the  filings  will  fall. 
Magnetism  produced  by  the  mere  presence  of  adjacent  magnets, 
unth  or  without  contact,  is  called  induced  magnetism.  If  the 
induced  magnetism  of  the  nail  in  Fig.  210  is  tested  with  a 
compass  needle,  it  is  found  that  the  remote  induced  pole  is 
of  the  same  kind  as  the  inducing  pole,  while  the  near  pole 
is  of  unlike  kind.  This  is  the  general  law  of  magnetic 
induction. 

Magnetic  induction  explains  the  fact  that  a  magnet  attracts 
an  unmagnetized  piece  of  iron,  for  it  first  magnetizes  it  by 
induction,  so  that  the  near  pole  is  unlike  the  inducing  pole, 
and  the  remote  pole  like  the  inducing  pole ;  and  then,  since 
the  two  unlike  poles  are  closer  together  than  the  like  poles, 
the  attraction  overbalances  the  repulsion  and  the  iron  is 
drawn  toward  the  magnet.  Magnetic  induction  also  explains 
the  formation  of  the  tufts  of  iron  filings  shown  in  Fig.  207, 
each  little  filing  becoming  a  temporary  magnet  such  that 
the  end  which  points  toward  the  inducing  pole  is  unlike 
this  pole,  and  the  end  which  points  away  from  it  is  like  this 
pole.  The  bushlike  appearance  is  due  to  the  repulsive  action 
which  the  outside  free  poles  exert  upon  each  other. 

268.  Retentivity  and  permeability.  A  piece  of  soft  iron 
will  very  easily  become  a  strong  temporary  magnet,  but  when 
removed  from  the  influence  of  the  magnet  it  loses  practically 
all  of  its  magnetism.  On  the  other  hand,  a  piece  of  steel 
will  not  be  so  strongly  magnetized  as  the  soft  iron,  but  it 
will  retain  a  much  larger  fraction  of  its  magnetism  after  it 
is  removed  from  the  influence  of  the  permanent  magnet. 
This  quality  of  resisting  either  magnetization  or  demagnetiza- 
tion is  called  retentivity.  Thus  steel  has  a  much  greater  reten- 
tivity  than  wrought  iron,  and,  in  general,  the  harder  the  steel 
the  greater  its  retentivity. 


218 


MAGNETISM 


A  substance  which  has  the  property  of  becoming  strongly 
magnetic  under  the  influence  of  a  permanent  magnet,  whether 
it  has  a  high  retentivity  or  not,  is  said  to  possess  permeability  in 
large  degree.  Thus  iron  is  much  more  permeable  than  nickel. 

269.  Magnetic  lines  of  force.  If  we  could  separate  the  N 
and  S  poles  of  a  small  magnet  so  as  to  get  an  independent 
N  pole,  and  were  to  place  this 
N  pole  near  the  N  pole  of  a  bar 
magnet,  it  would  move  over  to 
the  S  pole  along  some  curved 
path  similar  to  that  shown  in 

Fig.  211.     The  reason  it  would    FlG"  21^  A  line  of  force  set  up 

by  the  magnet  AB 
move  in  a  curved  path  is  that  it 

would  be  simultaneously  repelled  by  the  N  pole  of  the  bar 
magnet  and  attracted  by  its  S  pole,  and  the  relative  strengths 
of  these  two  forces  would  continually  change  as  the  relative 
distances  of  the  moving  pole  from  these  two  poles  changed. 

To  verify  this  conclusion  let  a  strongly  magnetized  sewing  needle  be 
floated  in  a  small  cork  in  a  shallow  dish  of  water,  and  let  a  bar  or 
horseshoe  magnet  be  placed  just 
above  or  just  beneath  the  dish  (see 
Fig.  212).  The  cork  and  needle  will 
then  move  as  would  an  independent 
pole,  since  the  remote  pole  of  the 
needle  is  so  much  farther  from  the 
magnet  than  the  near  pole  that  its 
influence  on  the  motion  is  very  small. 
The  cork  will  actually  be  found  to  move  in  a  curved  path  from  N  to  S. 

Any  path  which  an  independent  N  pole  would  take  in 
going  from  N  to  S  is  called  a  line  of  force.  The  simplest  way 
of  finding  the  direction  of  this  path  at  any  point  near  a 
magnet  is  to  hold  a  short  compass  needle  at  the  point  con- 
sidered. The  needle  sets  itself  along  the  line  in  which  its 
poles  would  move  if  independent,  that  is,  along  the  line  of 
force  which  passes  through  the  given  point  (see  C,  Fig.  211). 


FIG.  212.    Showing   direction   of 

motion  of   an  isolated  pole  near 

a  magnet 


GENERAL  PROPERTIES  OF  MAGNETS 


219 


270.  Fields  of  force.  The  region  about  a  magnet  in  which 
its  magnetic  forces  can  be  detected  is  called  its  field  of  force. 
The  easiest  way  of  gaining  an  idea  of  the  way  in  which  the 


\  !      /  /V""^,\  UN  \  '.  ' 
/  //  ,.-*— ,N\\  \  \  \  \  i  / , 

x^^  \\  (•( 'iff' ''"    ~^N\\V< :  \$M& 


FIG.  213.    Arrangement  of  iron 
filings  about  a  bar  magnet 


FIG.  214.    Ideal  diagram  of  field 
of  a  bar  magnet 


lines  of  force  are  arranged  in  the  magnetic  field  about  any 
magnet  is  to  sift  iron  filings  upon  a  piece  of  paper  placed 
immediately  over  the  magnet.  Each  little  filing  becomes  a 
temporary  magnet  by  induction,  and  therefore,  like  the  com- 
pass needle,  sets  itself  in  the  direction  of  the  line  of  force  at 
the  point  where  it  is.  Fig.  213 
shows  how  the  filings  arrange 
themselves  about  a  bar  magnet. 
Fig.  214  is  the  corresponding 
ideal  diagram  showing  the  lines 
of  force  emerging  from  the  JV" 
pole  and  passing  about  in  curved 
paths  to  the  S  pole.  It  is  custom- 
ary to  imagine  these  lines  as  re- 
turning through  the  magnet  from 
S  to  N  in  the  manner  shown,  so 
that  each  line  is  thought  of  as  a  closed  curve.  This  conven- 
tion was  introduced  by  Faraday,  and  has  been  found  of 
great  assistance  in  correlating  the  facts  of  magnetism. 

A  magnetic  field  of  unit  strength  is  defined  as  a  field  in  which 
a  unit  magnet  pole  experiences  1  dyne  of  force.    It  is  customary 


FIG.  215.  The  strength  of  a  mag- 
netic field  is  represented  by  the 
number    of   lines  of    force    per 
square   centimeter 


220  MAGNETISM 

to  represent  graphically  such  a  field  by  drawing  one  line  per 
square  centimeter  through  a  surface  such  as  ABCD  (Fig.  215) 
taken  at  right  angles  to  the  lines  of  force.  If  a  unit  N  pole  be- 
tween N  and  S  (Fig.  215)  were  pushed  toward  S  with  a  force 
of  1000  dynes,  the  strength  of  the  field  would  be  1000  units  and 
it  would  be  represented  by  1000  lines  per  square  centimeter. 

271.  Molecular  nature  of  magnetism.  If  a  small  test  tube 
full  of  iron  filings  be  stroked  from  end  to  end  with  a  magnet, 
it  will  be  found  to  have  become  itself  a  magnet  ;  but  it  will 
lose  its  magnetism  as  soon  as  the  filings  are  shaken  up.  If  a 
magnetized  knitting  needle  is  heated  red-hot,  it  will  be  found 
to  have  lost  its  magnetism  completely.  Again,  if  such  a  needle 
is  jarred,  or  hammered,  or  twisted,  the  strength  of  its  poles, 
as  measured  by  their  ability  to  pick  up  tacks  or  iron  filings, 
will  be  found  to  be  greatly  diminished. 

These  facts  point  to  the  conclusion  that  magnetism  has 
something  to  do  with  the  arrangement  ~of  the  molecules,  since 
causes  which  violently  dis- 
turb the  molecules  of  a  mag- 


net  weaken   its  magnetism.       Jf  Jja    ff 


Again,  if  a  magnetized  needle     £  —  &  I       %  $  —  4 

is  broken,   each  part  will   be      FIG.  210.   Effect  of  breaking  a  magnet 

found  to  be  a  complete  mag- 

net; that  is,  two  new  poles  will  appear  at  the  point  of  breaking. 
a  new  N  pole  on  the  part  which  has  the  original  S  pole,  and 
a  new  S  pole  on  the  part  which  has  the  original  N  pole.  The 
subdivision  may  be  continued  indefinitely,  but  always  with 
the  same  result,  as  indicated  in  Fig.  216.  This  suggests  that 
the  molecules  of  a  magnetized  bar  may  themselves  be  little 
magnets  arranged  in  rows  with  their  opposite  poles  in  contact. 
If  an  unmagnetized  piece  of  hard  steel  is  pounded  vigorously 
while  it  lies  between  the  poles  of  a  magnet,  or  if  it  is  heated 
to  redness  and  then  allowed  to  cool  in  this  position,  it  will 
be  found  to  have  become  magnetized.  This  suggests  that  the 


GENEEAL  PKOPERTIES  OF  MAGNETS     221 

molecules  of  the  steel  are  magnets  even  when  the  bar  as  a 
whole  is  not  magnetized,  and  that  magnetization  may  consist 
in  causing  them  to  arrange  themselves  in  rows,  end  to  end, 
just  as  the  magnetization  of  the  tube  of  iron  filings  mentioned 
above  was  due  to  a  special  arrangement  of  the  filings. 

272.  Theory  of  magnetism.  In  an  unmagnetized  bar  of  iron 
or  steel  it  is  probable,  then,  that  the  molecules  themselves  are 
tiny  magnets  which  are 
arranged  either  haphaz- 
ard or  in  little  closed 
groups  or  chains,  as  in 
Fig.  217,  SO  that,  011  the  FlG-  21L  Arrangement  of  molecules  in  an 

unmagnetized  iron  bar 
whole,    opposite    poles 

neutralize  each  other  throughout  the  bar.    But  when  the  bar 
is  brought  near  a  magnet,  the  molecules  are  swung  around 
by  the  outside  magnetic  force  into  an  arrangement  somewhat 
like  the  one  shown  in 
Fig.  218,  where  the  op- 
posite poles  completely 
neutralize    each    other 
only  in  the  middle  of       FIG  21g    Arrangement  of  molecules  in  a 
the  bar.    According  to  magnetized  iron  bar 

this  view,  heating  and 

jarring  weaken  the  magnet  because  they  tend  to  shake  the 
molecules  out  of  alignment.  On  the  other  hand,  heating  and 
jarring  facilitate  magnetization  when  the  bar  is  between  the 
poles  of  a  magnet  because  they  assist  the  magnetizing  force 
in  breaking  up  the  molecular  groups  and  chains  and  getting 
the  molecules  into  alignment.  Soft  iron  has  higher  permea- 
bility than  hard  steel,  because  the  molecules  of  the  former 
substance  are  much  easier  to  swing  into  alignment  than  those 
of  the  latter  substance.  Steel  has  a  very  much  greater  re- 
tentivity  than  soft  iron,  because  its  molecules  are  not  so  easily 
moved  out  of  position  when  once  they  have  been  aligned. 


\ 


222  MAUNETISM 

273.  Saturation.  Strong  evidence  for  the  correctness  of 
the  above  view  is  found  in  the  fact  that  a  piece  of  iron  or 
steel  cannot  be  magnet- 
ized beyond  a  certain 
limit,  no  matter  how 
strong  the  magnetizing 


cm  CM  cm  cm  cm  cm  CM  CM  cm  cm  cm  am  cm  annum  ami  an 

as  an  am  an  am  am  cm  am  cm  an  cm  nm  cm  cannon  am 

aicmizmcMcnaBCMcraca 

cm  en  an  ami  OB  an  cm  cm  ami  a"  rm  OB  axemen  am  cm  I 


force    is.      This    limit       ,, 

FIG.  219.  Arrangement  of  molecules  m  a 

probably  corresponds  to  saturated  magnet 

the  condition  in  which 

the  axes  of  all  the  molecules  are  brought  into  parallelism, 

as  in  Fig.  219.     The  magnet   is  then  said  to   be  saturated, 

since  it  is  as  strong  as  it  is  possible  to  make  it. 

TERRESTRIAL  MAGNETISM 

274.  The  earth's  magnetism.  The  fact  that  a  compass  needle 
always  points  north  and  south,  or  approximately  so,  indicates 
that  the  earth  itself  is  a  great  magnet  having  an  8  pole  near 
the  geographic  north  pole  and  an  N  pole  near  the  geographic 
south  pole ;  for  the  magnetic  pole  of  the  earth  which  is  near 
the  geographic  north  pole  must  of  course  be  unlike  the  pole 
of  a  suspended  magnet  which  points  toward  it,  and  the  pole 
of  the  suspended  magnet  which  points  toward  the  north  is  the 
one  which,  by  convention,  it  has  been  decided  to  call  the  JVpole. 
The  magnetic  pole  of  the  earth  which  is  near  the  north  geo- 
graphic  pole   was    found    in    1831    by    Sir  James    Ross   in 
Boothia  Felix,  Canada,  latitude  70°  30'  N.,  longitude  95°  W. 
It  was  located  again  in  190.5  by  Captain  Amundsen  (the  dis- 
coverer of  the  geographic  south  pole,   1912)    at   a  point   a 
little  farther  west.    Its  approximate  location  is  70°  5'  N.  and 
96°  46'  W.    It  is  probable  that  it  shifts  its  position  slowly. 

275.  Declination.    The  earliest  users  of  the  compass  were 
aware  that  it  did  not  point  exactly  north;  but  it  was  Columbus 
who,  on  his  first  voyage  to  America,  made  the  discovery,  much 
to  the  alarm  of  his  sailors,  that  the  direction  of  the  compass 


WILLIAM  GILBERT  (1540-1603) 

English  physician  and  physicist;  first  Englishman  to  appreciate 
fully  the  value  of  experimental  observations;  first  to  discover 
through  careful  experimentation  that  the  compass  points  to  the 
north  not  because  of  some  influence  of  the  stars,  but  because  the 
earth  is  itself  a  great  magnet ;  first  to  use  the  word  "  electricity  " ; 
first  to  discover  that  electrification  can  be  produced  by  rub- 
bing a  great  many  different  kinds  of  substances ;  author  of  the 
epoch-making  book  entitled  "De  Magnete,  etc.,"  published  in 
London  in  1600 


TEKKESTRIAL  MAGNETISM  223 

needle  changes  as  one  moves  about  over  the  earth's  surface. 
The  chief  reason  for  this  variation  is  found  in  the  fact  that  the 
magnetic  poles  do  not  coincide  with  the  geographic  poles ; 
but  there  are  also  other  causes,  such  as  the  existence  of  large 
deposits  of  iron  ore,  which  produce  local  effects  upon  the 
needle.  The  number  of  degrees  by  which  at  a  given  point  on 
the  earth  the  needle  varies  from  a  true  north-and-south  line  is 
called  its  declination  at  that  point.  Lines  drawn  over  the  earth 
through  points  of  equal  declination  are  called  isogonic  lines. 

276.  The  dipping  needle.    Let  an  umnagnetized  knitting  needle  a 
(Fig.  220)  be  thrust  through  a  cork,  and  let  a  second  needle  b  be  passed 
through  the  cork  at  right  angles  to  a  and  as 

close  to  it  as  possible.   Let  a  pin  c  be  adjusted 

until   the    system    is    in    neutral    equilibrium 

about  b  as  an  axis,  when  a  is  pointing  east  and 

west.    Then  let  a  be  carefully  magnetized  by 

stroking  one  end  of  it,  from  the  middle  out,     FJG  22Q     Arrangement 

with  the  N  pole  of  a  strong  magnet,  and  the  for  s}lowing  dip 

other  end,  from  the  middle  out,  with  the  S 

pole  of  the  same  magnet.   If  now  the  needle  is  replaced  on  its  supports 

and  turned  into  a  north-and-south  position,  its  N  pole  will  be  found 

to  dip  so  as  to  cause  the  needle  to  make  an  angle  of  from  60°  to  70° 

with  the  horizontal. 

The  experiment  shows  that  in  this  latitude  the  earth's  mag- 
netic lines  make  a  large  angle  with  the  horizontal.  This  angle 
between  the  earth's  surface  and  the  direction  of  the  magnetic 
lines  is  called  the  dip,  or  inclination,  of  the  needle.  At  Wash- 
ington it  is  71°  5'  and  at  Chicago  72°  50V  At  the  magnetic 
pole  it  is  of  course  90°,  and  at  the  so-called  magnetic  equator, 
which  is  an  irregular  curved  line  near  the  geographic  equator, 
the  dip  is  0°. 

277.  The  earth's  inductive  action.    That  the  earth  acts  like  a 
great  magnet  may  be  very  strikingly  shown  in  the  following  way : 

Hold  a  steel  rod  (for  example,  a  tripod  rod)  parallel  to  the  earth's 
magnetic  lines  (the  north  end  slanting  down  at  an  angle  of  about  70° 
or  75°)  and  strike  it  a  few  sharp  blows  with  a  hammer.  The  rod  will 


224  MAGNETISM 

be  found  to  have  become  a  magnet  with  its  upper  end  an  S  pole,  like 
the  north  pole  of  the  earth,  and  its  lower  end  an  N  pole.  If  the  rod  is 
reversed  and  tapped  again  with  the  hammer,  its  magnetism  will  be  re- 
versed. If  held  in  an  east-and-west  position  and  tapped,  it  will  become 
demagnetized,  as  will  be  shown  by  the  fact  that  either  end  of  it  will 
attract  either  end  of  a  compass  needle.  In  some  respects  a  soft-iron  rod 
is  more  satisfactory  for  this  experiment  than  a  steel  rod,  on  account  of 
the  smaller  retentivity. 

QUESTIONS  AND  PROBLEMS 

1.  Make  a  diagram  to  show  the  general  shape  of  the  lines  of  force 
between  unlike  poles  of  two  bar  magnets ;  between  like  poles. 

2.  Devise  an  experiment  which  will  show  that  a  piece  of  iron  attracts 
a  magnet  just  as  truly  as  the  magnet  attracts  the  iron. 

3.  In  testing  a  needle  with  a  magnet  to  see  if  the  needle  is  magnet 
ized  why  must  you  get  repulsion  before  you  can  be  sure  it  is  magnetized? 

4.  A  nail  lies  with  its  head  near  the  N  pole  of  a  bar  magnet. 
Diagram  the  nail  and  magnet,  and  draw  from  the  N  pole  through  the 
nail  a  closed  curve  to  represent  one  line  of  force. 

5.  Explain,  on  the  basis  of  induced  magnetization,  the  process  by 
which  a  magnet  attracts  a  piece  of  soft  iron. 

6.  Do  the  facts  of  induction  suggest  to  you  any  reason  why  a  horse- 
shoe magnet  retains  its  magnetism  better  when  a  bar  of  soft  iron  (a 
keeper,  or  armature)  is  placed  across  its  poles  than  when  it  is  not  so 
treated?    (See  Fig.  218.) 

7.  Why  should  the  needle  used  in  the  experiment  of  §  276  be  placed 
east  and  west,  when  adjusting  for  neutral  equilibrium,  before  it  is 
magnetized  ? 

8.  How  would  an  ordinary  compass  needle  act  if  placed  over  one  of 
the  earth's  magnetic  poles  ?    How  would  a  dipping  needle  act  at  these 
points  ? 

9.  Why  are  the  tops  of  steam  radiators  £  magnetic  poles,  as  proved 
by  their  invariable  repulsion  of  the  5  pole  of  a  compass  ? 

10.  Give  two  proofs  that  the  earth  is  a  magnet. 

11.  A  magnetic  pole  of  80  units'  strength  is  20  cm.  distant  from  a 
similar  pole  of  30  units'  strength.    Find  the  force  between  them. 


CHAPTER  XIII 

STATIC  ELECTRICITY 

GENERAL  FACTS  OF  ELECTRIFICATION 

278.  Electrification  by  friction.  If  a  piece  of  hard  rubber  or 
a  stick  of  sealing  wax  is  rubbed  with  flannel  or  cat's  fur  and 
then  brought  near  some  dry  pith  balls,  bits  of  paper,  or  other 
light  bodies,  these  bodies  are  found  to  jump  toward  the  rod. 
This  sort  of  attraction,  so  familiar  to  us  from  the  behavior  of 
our  hair  in  winter  when  we  comb  it  with  a  rubber  comb,  was 
observed  as  early  as  600  B.  c.,  when  Thales  of  Greece  com- 
mented upon  the  fact  that  rubbed  amber  draws  to  itself  threads 
and  other  light  objects.  It  was  not,  however,  until  A.  D.  1600 
that  Dr.  William  Gilbert,  physician  to  Queen  Elizabeth,  and 
sometimes  called  the  father  of  the  modern  science  of  electricity 
and  magnetism,  discovered  that  the  effect  could  be  produced 
by  rubbing  together  a  great  variety  of  other  substances  besides 
amber  and  silk,  such,  for  example,  as  glass  and  silk,  sealing 
wax  and  flannel,  hard  rubber  and  cat's  fur,  etc. 

Gilbert  (see  opposite  p.  222)  named  the  effect  which  was 
produced  upon  these  various  substances  by  friction  electrifi- 
cation, after  the  Greek  name  electron,  meaning  "  amber."  Thus, 
a  body  ivhich,  like  rubbed  amber,  has  been  endowed  with  the 
property  of  attracting  light  bodies  is  said  to  have  been  electrified, 
or  to  have  been  given  a  charge  of  electricity.  In  this  statement 
nothing  whatever  is  said  about  the  nature  of  electricity.  We 
simply  define  an  electrically  charged  body  as  one  which  has 
been  put  into  the  condition  in  which  it  acts  toward  light 
bodies  like  the  rubbed  amber  or  the  rubbed  sealing  wax.  To 

225 


226  STATIC  ELECTRICITY 

this  day  we  do  not  know  with  certainty  what  the  nature  of 
electricity  is,  but  we  are  fairly  familiar  with  the  laws  which 
govern  its  action.  The  following  sections  deal  with  these  laws. 

279.  Positive  and  negative  electricity.  Let  a  pith  ball  suspended 
by  a  silk  thread,  as  in  Fig.  221,  be  touched  to  a  glass  rod  which  has  been 
rubbed  with  silk ;  the  ball  will  thus  be  put  into  the  condition  in  which 
it  is  strongly  repelled  by  this  rod. 
Next  let  a  stick  of  sealing  wax  or  an 
ebonite  rod  which  has  been  rubbed 
with  cat's  fur  or  flannel  be  brought 
near  the  charged  ball.    It  will  be 
found  that  it  is  not  repelled  but,  on 
the  contrary,  is  very  strongly  at- 
tracted.   Similarly,  if  the  pith  ball 
has  touched  the  sealing  wax  so  that 
it  is  repelled  by  it,  it  is  found  to  be         FIG.  221.    Pith-ball  electroscope 
strongly  attracted  by  the  glass  rod. 

Again,  two  pith  balls  both  of  which  have  been  in  contact  with  the 
glass  rod  are  found  to  repel  each  other,  while  pith  balls  one  of  which 
has  been  in  contact  with  the  glass  rod  and  the  other  with  the  sealing 
wax  attract  each  other. 

Evidently,  then,  the  electrifications  which  are  imparted  to 
glass  by  rubbing  it  with  silk  and  to  sealing  wax  by  rubbing 
it  with  flannel  are  opposite  in  the  sense  that  an  electrified 
body  that  is  attracted  by  one  is  repelled  by  the  other.  We 
say,  therefore,  that  there  are  two  kinds  of  electrification,  and 
we  arbitrarily  call  one  positive  and  the  other  negative.  Thus,  a 
positively  electrified  body  is  one  which  acts  with  respect  to  other 
electrified  bodies  like  a  glass  rod  which  has  been  rubbed  with 
silk,  and  a  negatively  electrified  body  is  one  which  acts  like  a 
piece  of  sealing  wax  which  has  been  rubbed  with  flannel.  These 
facts  and  definitions  may  be  stated  in  the  following  general 
law:  Electrical  charges  of  like  kind  repel  each  other,  while 
charges  of  unlike  kind  attract  each  other.  The  forces  of  attrac- 
tion or  repulsion  are  found,  like  those  of  gravitation  and 
magnetism,  to  decrease  as  the  square  of  the  distance  increases. 


GENERAL  FACTS  OF  ELECTRIFICATION        227 


280.  Measurement  of  electrical  quantities.    The  fact  of  attraction  and 
repulsion  is  taken  as  the  basis  for  the  definition  and  measurement  of 
so-called  quantities  of  electricity.    Thus,  a  small  charged  body  is  said  to 
contain  1  unit  of  electricity  when  it  will  repel  an  exactly  equal  and 
similar  charge  placed  1  centimeter  away  with  a  force  of  1  dyne.    The 
number  of  units  of  electricity  on  any  charged  body  is  then  measured 
by  the  force  which  it  exerts  upon  a  unit  charge  placed  at  a  given  distance 
from  it;  for  example,  a  charge  wrhich  at  a  distance  of  10  centimeters 
repels  a  unit  charge  with  a  force  of  1  dyne  contains  100  units  of  elec- 
tricity, for  this  means  that  at  a  distance  of  1  centimeter  it  would  repel 
the  unit  charge  writh  a  force  of  100  dynes  (see  §  279). 

281.  Conductors  and    nonconductors.    Let  an  electroscope  E 

(Fig.  222),  consisting  of  a  pair  of  gold  leaves  a  and  ft,  suspended  from 

an  insulated  metal  rod  r  and  protected  from  air  currents  by  a  case  «/, 

be  connected  with  the  metal  ball 

B  by  means  of  a  wire.    Now  let 

an  ebonite  rod  be  electrified  and 

rubbed  over  B.    The  immediate 

divergence  of  the  gold  leaves  will 

show  that  a  portion  of  the  electric 

charge  placed  upon  B  has  been 

carried  by  the  wire  to  the  gold 

leaves,  where  it  causes  them  to 

diverge  in   accordance   with   the 

law  that  bodies  charged  with  the 

same    kind    of    electricity    repel         FIG.  222.   Illustrating  conduction 

each  other. 

Let  the  experiment  be  repeated  when  E  and  B  are  connected  with  a 
thread  of  silk  or  a  long  rod  of  wood  instead  of  the  metal  wire.  No 
divergence  of  the  leaves  will  be  observed.  If  a  moistened  thread  con- 
nects E  and  B,  the  leaves  will  be  seen  to  diverge  slowly  when  the  ball  B 
is  charged,  showing  that  a  charge  is  carried  slowly  by  the  moist  thread. 

These  experiments  .make  it  clear  that  while  electric  charges 
pass  with  perfect  readiness  from  one  point  to  another  in  a  wire, 
they  are  quite  unable  to  pass  along  dry  silk  or  wood,  and  pass 
with  difficulty  along  moist  silk.  We  are  therefore  accustomed 
to  divide  substances  into  two  classes,  conductors  and  noncon- 
ductors, or  insulators,  according  to  their  ability  to  transmit 


A 


228 


STATIC  ELECTRICITY 


electrical  charges  from  point  to  point.  Thus,  metals  and 
solutions  of  salts  and  acids  in  water  are  all  conductors  of 
electricity,  while  glass,  porcelain,  rubber,  mica,  shellac,  wood, 
silk,  vaseline,  turpentine,  paraffin,  and  oils  are  insulators.  No 
hard-aid-fast  line,  however,  can  be  drawn  between  conduc- 
tors and  nonconductors,  since  all  so-called  insulators  conduct 
to  some  slight  extent,  while  the  so-called  conductors  differ 
greatly  in  the  facility  with  which  they  transmit  charges. 

The  fact  of  conduction  brings  out  sharply  one  of  the  most 
essential  distinctions  between  electricity  and  magnetism.  Mag- 
netic poles  exist  only  in  iron  and  steel,  while  electrical  charges 
may  be  communicated  to  any  body  whatever,  provided  it  is 
insulated.  These  charges  pass  over  conductors  and  can  be 
transferred  by  contact  from  one 
body  to  any  other,  while  mag- 
netic poles  remain  fixed  in  posi- 
tion and  are  wholly  uninfluenced 
by  contact  with  other  bodies, 
unless  these  bodies  themselves 
are  magnets. 


FIG.  223.    Illustrating  induction 


282.   Electrostatic   induction. 

Let  the  ebonite  rod  be  electrified  by 

friction  and  slowly  brought  toward 

the  knob  of  the  gold-leaf  electroscope  (Fig.  223).   The  leaves  will  be 

seen  to  diverge,  even  though  the  rod  does  not  approach  to  within  a  foot 

of  the  electroscope. 

This  makes  it  clear  that  the  mere  influence  which  an  electric 
eharge  exerts  upon  a  conductor  placed  in  its  neighborhood  is 
able  to  produce  electrification  in  that  conductor.  This  method 
of  producing  electrification  is  called  electrostatic  induction. 

As  soon  as  the  charged  rod  is  removed,  the  leaves  will  be 
seen  to  collapse  completely.  This  shows  that  this  form  of  elec- 
trification is  only  a  temporary  phenomenon  which  is  due  simply 
to  the  presence  of  the  charged  body  in  the  neighborhood. 


GENEKAL  FACTS  OF  ELECTRIFICATION        229 
283.  Nature  of  electrification  produced  by  induction.    Let  a 

metal  ball  A  (Fig.  224)  be  strongly  charged  by  rubbing  it  with  a  charged 
rod,  and  let  it  then  be  brought  near  an  insulated*  metal  body  B  which 
is  provided  with  pith  balls  or  strips  of  paper  a,  b,  c,  as  shown.  The  di- 
vergence of  a  and  c  will  show  that  the  ends  of  B  have  received  electrical 
charges  because  of  the  presence  of 
A,  while  the  failure  of  b  to  diverge  /"  "N  o. 


.  _    _ 

will  show  that  the   middle  of   £   is       (    +    )    Cl  _  ?  _  t) 
uncharged.     Further,  the  rod  which 

charged  A  will  be  found  to  repel  c         FIG.  224.    Nature  of  induced 
but  to  attract  a.  charges 

We  conclude,  therefore,  that  when  a  conductor  is  brought 
near  a  charged  body,  the  end  away  from  the  inducing  charge 
is  electrified  with  the  same  kind  of  electricity  as  that  on  the  in- 
ducing body,  while  the  end  toward  the  inducing  body  receives 
electricity  of  the  opposite  kind. 

284.  The  electron  theory  of  electricity.  The  atoms  of  all 
substances  are  now  known  to  contain  as  constituents  both 
positive  and  negative  electricity,  the  latter  existing  in  the  form 
of  minute  corpuscles,  or  electrons,  each  of  which  has  a  mass 
1  8*  of  that  of  the  hydrogen  atom.  These  electrons  are 
probably  grouped  in  some  way  about  the  positive  electricity 
as  a  nucleus.  The  sum  of  the  negative  charges  of  these  elec- 
trons is  supposed  to  be  just  equal  to  the  positive  charge  of 
the  nucleus,  so  that  in  its  normal  condition  the  whole  atom  is 
neutral,  or  uncharged.  But  in  conductors  electrons  are  con- 
tinually getting  loose  from  the  atoms  and  reentering  other 
atoms,  so  that  at  any  given  instant  there  are  in  every  con- 
ductor a  number  of  free  negative  electrons  and  a  correspond- 
ing number  of  atoms  which  have  lost  electrons  and  which 
are  therefore  positively  charged.  Such  a  conductor  would,  as  a- 
whole,  show  no  charge  of  either  positive  or  negative  electricity. 

*  Sulphur  is  practically  a  perfect  insulator  in  all  weathers,  wet  or  dry. 
Metal  conductors  of  almost  any  shape  resting  upon  pieces  of  sulphur  will 
serve  the  purposes  of  this  experiment  in  summer  or  winter. 


230  STATIC  ELECTRICITY 

But  as  soon  as  a  body  charged,  for  example,  positively 
(Fig.  224)  is  brought  near  su^h  a  conductor,  the  negatively 
charged  electrons  are  attracted  to  the  near  end,  leaving  behind 
them  the  positively  charged  atoms,  which  are  not  free  to  move 
from  their  positions.  On  the  other  hand,  if  a  negatively  charged 
body  is  brought  near  the  conductor,  the  negative  electrons 
stream  away  and  the  near  end  is  left  with  the  immovable  plus 
atoms.  As  soon  as  the  inducing  charge  is  removed,  the  con- 
ductor becomes  neutral  again,  because  the  little  negative  cor- 
puscles return  to  their  former  positions  under  the  influence  of 
the  attraction  of  the  positive  atoms.  This  is  the  present-day 
picture  of  the  mechanism  of  electrification  by  induction. 

The  charge  of  one  electron  is  called  the  elementary  electrical 
charge.  Its  value  has  recently  been  accurately  measured. 
There  are  2.095  billion  of  them  in  one  of  the  units  denned  in 
§  280.  Every  electrical  charge  consists  of  an  exact  number  of 
these  ultimate  electrical  atoms. 

285 .  Charging  by  induction.  Let  two  metal  balls  or  two  eggshells, 
A  and  B,  which  have  been  gilded  or  covered  with  tin  foil  be  suspended 
by  silk  threads  and  touched  together,  as  in  Fig.  225.  Let  a  positively 
charged  body  C  be  brought  near  them. 
As  described  above,  A  and  B  will  at  once 
exhibit  evidences  of  electrification ;  that 
is,  A  will  repel  a  positively  charged  pith 
ball,  while  B  will  attract  it.  If  C  is  re- 
moved while  A  and  B  are  still  in  contact, 
the  separated  charges  reunite  and  A  and 

B  cease  to  exhibit  electrification.    But  if 

FIG.  22o.     Obtaining   a 
A  and  B  are  separated  from  each  other          plug  ftnd  a  mmug  chftrge 

while  C  is  in  place,  A  will  be  found  to  bv  in(juctiOn 

remain  positively  charged  and  B  nega- 
tively charged.  This  may  be  proved  either  by  the  attractions  and  repul- 
sions which  they  show  for  charged  rods  brought  near  them  or  by  the 
effects  which  they  produce  upon  a  charged  electroscope  brought  into 
their  vicinity,  the  leaves  of  the  latter  falling  together  when  it  is  brought 
near  one  and  spreading  farther  apart  when  brought  near  the  other. 


BENJAMIN  FRANKLIN  (1706-1790) 

Celebrated  American  statesman,  philosopher,  and  scientist;  born 
at  Boston,  the  sixteenth  child  of  poor  parents ;  printer  and  pub- 
lisher by  occupation;  pursued  scientific  studies  in  electricity  as 
a  diversion  rather  than  as  a  profession ;  first  proved  that  the  two 
coats  of  a  Leyden  jar  are  oppositely  charged;  introduced  the 
terms  positive  and  negative  electricity;  proved  the  identity  of 
lightning  and  frictional  electricity  by  flying  a  kite  in  a  thunder- 
storm and  drawing  sparks  from  the  insulated  lower  end  of  the 
kite  string ;  invented  the  lightning  rod ;  originated  the  one-fluid 
theory  of  electricity  which  regarded  a  positive  charge  as  indi- 
cating an  excess,  a  negative  charge  a  deficiency,  in  a  certain 
normal  amount  of  an  all-pervading  electrical  fluid 


FRANKLIN'S  KITE  EXPERIMENT 

In  June,  1752,  Franklin  demonstrated  the  identity  of  the  electric  spark  and  light- 
ning. To  prevent  his  kite  from  being  torn  in  the  rain  he  made  it  of  a  silk  handker- 
chief. The  lower  end  of  the  kite  string  and  a  silk  ribbon  were  tied  to  the  ring  of  a 
key,  and,  to  prevent  any  charge  that  might  appear  upon  the  string  and  the  key  from 
escaping  through  his  body  to  the  earth,  he  held  the  kite  by  grasping  the  insulating 
silk  ribbon.  Standing  under  a  shed  to  keep  the  ribbon  dry,  Franklin,  by  presenting 
his  knuckle  to  the  key,  obtained  sparks  similar  to  those  produced  by  his  electric 
machine.  With  these  sparks  he  charged  his  Leyden  jar  and  used  it  to  give  a  shock. 
Indeed,  he  performed  with  lightning  all  the  experiments  which  he  had  previously 
performed  with  sparks  from  his  frictional  machine.  The  experiment  is  dangerous 
and  should  not  be  attempted  by  inexperienced  persons 


GENERAL  FACTS  OF  ELECTRIFICATION        231 

We  see,  therefore,  that  if  tve  cut  in  two,  or  separate  into 
two  parts,  a  conductor  while  it  is  under  the  influence  of  an 
electric  charge,  ive  obtain  two  permanently  charged  bodies,  the 
remoter  part  having  a  charge  of  the  same  sign  as  that  of  the 
inducing  charge,  and  the  near  part  having  a  charge  of  unlike 
sign.  Under  the  influence  of  the  positive  charge  on  C  the 
negative  electrons  moved  out  of  A  into  B,  which  act  made  A 
positive  and  B  negative. 

Let  the  conductor  R  (Fig.  226)  be  touched  at  a  by  -the  finger  while  a 
charged  rod  C  is  near  it.  Then  let  the  finger  be  removed  and  after  it 
the  rod  C.  If  now  a  negatively  charged  pith  ball  is  brought  near  B,  it 
will  be  repelled,  showing  that  B 

has  become  negatively  charged.   In       («+  B  -a) 

this  experiment  the   body   of  the 
experimenter    corresponds   to    the 

egg  A  of  the  preceding  experiment^     ^  m    A  fe  d 

and  removing  the   finger  from  B     ti(m  hag  ft  charge  Qf  ^  Qpposite 
corresponds  to  separating  the  two  that  of  the  inducing  charge 

eggshells.     Let    the    last    experi- 
ment be  repeated  with  only  this  modification,  that  B  is  touched  at 
b  rather  than  at  a.    When  B  is  again  tested  with  the  pith  ball,  it  will 
still  be  found  to  have  a  negative  charge,  exactly  as  when  the  finger 
was  touched  at  a. 

We  conclude,  therefore,  that  no  matter  where  the  body 
B  is  touched,  the  sign  of  the  charge  left  upon  it  is  always 
opposite  to  that  of  the  inducing  charge.  This  is  because  the 
negative  electricity,  that  is,  the  electrons,  can  under  no 
circumstances  escape  from  b  so  long  as  C  is  present,  for 
they  are  bound  by  the  attraction  of  the  positive  charge 
on  C.  Indeed,  the  final  negative  charge  on  B  is  due  merely 
to  the  fact  that  the  positive  charge  on  C  pulls  electrons  into 
B  from  the  finger,  no  matter  where  B  is  touched.  In  the 
same  way,  if  C  had  been  negative,  it  would  have  pushed 
electrons  off  from  B  through  the  finger  and  thus  have  left 
B  positively  charged. 


232  STATIC  ELECTRICITY 

286.  Charging  the  electroscope  by  induction.    Let  an  ebonite 

rod  which  has  been  rubbed  with  catskin  be  brought  near  the  knob  of 
the  electroscope  (Fig.  223).  The  leaves  at  once  diverge.  (Make  a  dia- 
gram of  the  electroscope  with  the  negatively  charged  ebonite  rod  near 
the  knob.  By  use  of  +  and  —  signs  explain  the  electrical  condition  of 
both  the  knob  and  the  leaves.)  Let  the  knob  be  touched  with  the  finger 
while  the  rod  is  held  in  place.  The  leaves  will  fall  together.  (Explain 
by  a  diagram  as  before.)  Let  the  finger  be  removed  and  then  the  rod. 
The  leaves  will  fly  apart  again.  (By  a  diagram  explain  the  final  elec- 
trical condition  of  both  the  knob  and  the  leaves.) 

The  electroscope  has  been  charged  by  induction,  and  since 
the  charge  on  the  ebonite  rod  was  negative,  the  charge  on 
the  electroscope  must  be  positive.  If  this  conclusion  is  tested 
by  bringing  the  charged  ebonite  rod  near  the  electroscope, 
the  leaves  will  fall  together  as  the  rod  approaches  the  knob. 
How  does  this  prove  that  the  charge  on  the  electroscope  is 
positive  ?  If  the  empty  neutral  hand  approaches  the  knob, 
the  leaves  diverge  less.  Explain. 

287.  Plus  and  minus  electricities  always  appear  simultane- 
ously and  in  equal   amounts.    Let  an  ebonite  rod  be  completely 
discharged  by  passing  it  quickly  through  a  Bunsen  flame.   Let  a  flannel 
cap  having  a  silk  thread  attached  be  slipped  over 

the  rod,  as  in  Fig.  227,  and  twisted  rapidly  around 
a  immber  of  times.  When  rod  and  cap  together 
are  held  near  a  charged  electroscope,  no  effect  will 
be  observed ;  but  if  the  cap  is  pulled  off,  it  will  be 
found  to  be  positively  charged,  while  the  rod  will 

be  found  to  have  a  negative  charge. 

FIG.  22 7.   Plus  and 

Since  the  two  together  produce  no  effect,  minus  electricities 
the  experiment  shows  that  the  plus  and  alwavs  developed 

in  equal  amounts 
minus  charges  were  equal  in  amount.    This 

experiment  confirms  the  view  already  brought  forward  in 
connection  with  induction,  that  electrification  always  consists 
in  a  separation  of  plus  and  minus  charges  which  already  exist 
in  equal  amounts  within  the  bodies  in  which  the  electrification 
is  developed. 


DISTRIBUTION  OF  CHARGE  233 


QUESTIONS  AND  PROBLEMS 

1.  If  pith  balls,  or  any  light  figures,  are  placed  between  two  plates 
(Fig.  228),  one  of  which  is  connected  to  earth  and  the  other  to  one  knob 
of  an  electrical  machine  in  operation,  the  figures  will  bound  back  and 
forth  between  the  two  plates  as  long  as  the  machine  is  operated.  Explain. 

2.  Given  a  gold-leaf  electroscope,  a  glass  rod,  and  a 
piece  of  silk,  how,  in  general,  would  you  proceed  to  test 
the  sign  of  the  electrification  of  an  unknown  charge? 

3.  Charge  a  gold-leaf  electroscope  by  induction  from 
a  glass  rod.    Warm  a  piece  of  paper  and  stroke  it  on 
the  clothing.    Hold  it  over  the  charged  electroscope. 
If  the  divergence  of  the  gold  leaves  is  increased,  is  the 
charge  on  the  paper  +   or  —  ?    If  the  divergence  is 
decreased,  what  is  the  sign  of  the  charge  on  the  paper  ? 

4.  If  you  are  given  a  positively  charged  insulated 

sphere,  how  could  you  charge  two  other  spheres,  one  positively  and  the 
other  negatively,  without  diminishing  the  charge  on  the  first  sphere? 

5.  If  you  bring  a  positively  charged  glass  rod  near  the  knob  of  an 
electroscope  and  then  touch  the  knob,  why  do  you  not  remove  the  nega- 
tive electricity  which  is  on  the  knob  ? 

6.  In  charging  an  electroscope  by  induction,  why  must  the  finger 
be  removed  before  the  removal  of  the  charged  body? 

7.  If  you  hold  a  brass  rod  in  the  hand  and  rub  it  with  silk,  the  rod 
will  show  no  sign  of  electrification ;  but  if  you  hold  the  brass  rod  with 
a  piece  of  sheet  rubber  and  then  rub  it  with  silk,  you  will  find  it  elec- 
trified.   Explain. 

8.  State  as  many  differences  as  you  can  between  the  phenomena  of 
magnetism  and  those  of  electricity. 

9.  If  an  electrified  rod  is  brought  near  to  a  pith  ball  siispended  by 
a  silk  thread,  the  ball  is  first  attracted  to  the  rod  and  then  repelled 
from  it.    Explain  this. 

DISTRIBUTION  OF  ELECTRIC   CHARGE  UPON  CONDUCTORS 

288.  Electric  charges  reside  only  upon  the  outside  surface  of 
conductors.  Let  a  deep  tin  cup  (Fig.  229)  be  placed  upon  an  insulating 
stand  and  charged  as  strongly  as  possible  either  from  an  ebonite  rod 
or  from  an  electrical  machine.  If  now  a  smooth  metal  ball  suspended  by  a 
silk  thread  is  touched  to  the  outside  of  the  charged  cup  and  then  brought 
near  the  knob  of  a  charged  electroscope,  it  will  show  a  strong  charge  ; 
but  if  it  is  touched  to  the  inside  of  the  cup,  it  will  show  no  charge  at  all. 


234 


STATIC  ELECTRICITY 


These  experiments  show  that  an  electric  charge  resides 
entirely  on  the  outside  surface  of  a  conductor.  This  is  a  result 
which  might  have  been  inferred  from 
the  fact  that  all  the  little  electrical 
charges  of  which  the  total  charge  is 
made  up  repel  each  other  and  there- 
fore move  through  the  conductor 
until  they  are,  on  the  average,  as 
far  apart  as  possible. 

289.  Density  of  charge  greatest 
where  curvature  of  surface  is  greatest. 
Since  all  of  the  parts  of  an  electric  charge  tend,  because  of 
their  mutual  repulsions,  to  get  as  far  apart  as  possible,  we 
should  infer  that  if  a  charge  of  either  sign  is  placed  upon  an 
oblong  conductor  like  that  of  Fig.  230,  (1),  it  will  distribute 
itself  so  that  the  electrification  at  the  ends  will  be  stronger 
than  that  at  the  middle. 


FIG.  229.   Proof  that  charge 
resides  on  surface 


(1) 


To  test  this  inference  let  a  proof  plane — a  flat  metal  disk  (for  example, 
a  cent)  provided  with  an  insulating  handle  —  be  touched  to  one  end  of 
such  a  charged  body,  the  charge  conveyed 
to  a  gold-leaf  electroscope,  and  the  amount 
of  separation  of  the  leaves  noted.  Then  let 
the  experiment  be  repeated  when  the  proof 
plane  touches  the  middle  of  the  body.  The 
separation  of  the  leaves  in  the  latter  case 
will  be  found  to  be  very  much  less  than  in 
the  former.  If  we  should  test  the  distribu- 
tion on  a  pear-shaped  body  (Fig.  230,  (2))  in 
the  same  way,  we  should  find  the  density  of 
electrification  considerably  greater  on  the 

small  end  than  on  the  large  one.    By  density  of  electrification  is  meant 
the  quantity  of  electricity  on  unit  area  of  the  surface. 

290.  Discharging  effect  of  points.  The  above  experiments 
indicate  that  if  one  end  of  a  pear-shaped  body  is  made  more 
and  more  pointed,  then,  when  the  body  is  charged,  the  electric 


FIG.  230.    Distribution  of 
charge  over  oblong  bodies 


DISTRIBUTION  OF  CHARGE  235 

density  on  this  end  will  become  greater  and  greater.  The  fol- 
lowing experiment  will  show  what  happens  when  the  conductor 
is  provided  with  a  sharp  point. 

Let  a  very  sharp  needle  be  attached  to  any  smooth  insulated  metal 
body  provided  with  paper  or  pith-ball  indicators,  as  in  Fig.  224,  p.  229. 
If  the  body  is  now  charged  either  with  a  rubbed  rod  or  with  an  electric 
machine,  as  soon  as  the  supply  of  electricity  is  stopped  the  paper  indi- 
cators will  immediately  fall,  showing  that  the  body  is  losing  its  charge. 
To  show  that  this  is  certainly  due  to  the  effect  of  the  point,  remove  the 
needle  and  repeat.  The  indicators  will  fall  very  slowly  if  at  all. 

The  experiment  shows  that  the  electrical  density  upon  the 
point  is  so  great  that  the  charge  escapes  from  it  into  the  air. 
This  is  because  the  intense  charge  on  the  point  causes  many 
of  the  adjacent  molecules  of  the  air  to  lose  an  electron.  This 
leaves  these  molecules  positively  charged.  The  free  electrons 
attach  themselves  to  neutral  molecules,  thus  charging  them 
negatively.  One  set  of  these  electrically  charged  molecules 
(called  ions)  is  attracted  to  the  point  and  the  other  repelled 
from  it.  The  former  set  move  to  the  conductor,  give  up 
their  charges  to  it,  and  thus  neutralize  the  charge  upon  it. 

The  effect  of  points  may  be  shown  equally  well  by  charging  the  gold- 
leaf  electroscope  and  holding  a  needle  in  the  hand  within  a  few  inches 
of  the  knob.    The  leaves  will  fall  together  rap- 
idly.   In  this  case  the  needle  point  becomes  elec- 
trified by  induction  and  discharges  to  the  knob 
electricity  of  the  opposite  kind  to  that  on  the 
knob,  thus  neutralizing  its  charge.    An  entertain- 
ing variation  of  the  last  experiment  is  to  attach 
a  tassel  of  tissue  paper  to  an  insulated  conductor     j,       031      Dischare1 
and  electrify  it  strongly.    The  paper   streamers       ing  effect  of  points 
under  their  mutual  repulsions  will  stand  out  in  all 

directions,  but  as  soon  as  a  needle  point  is  held  in  the  hand  near  them, 
they  will  fall  together  (Fig.  231),  being  discharged  as  described  above. 

291 .  The  electric  whirl.  Let  an  electric  whirl  (Fig.  232)  be  bal- 
anced upon  a  pin  point  and  attached  to  one  knob  of  an  electric  machine. 
As  soon  as  the  machine  is  started,  the  whirl  will  rotate  rapidly  in  the 
direction  of  the  arrows. 


236 


STATIC  ELECTRICITY 


FIG.  232.    The 
electric  whirl 


FIG.  233.    The  elec- 
tric wind 


The  explanation  is  as  follows :  The  air  close  to  each  point 
is  ionized,  as  explained  in  §  290.  The  ions  of  sign  unlike 
that  of  the  charge  on  the  point  are  drawn  to  the  point  and 
discharged.  The  other  set 
of  ions  is  repelled.  But 
since  this  repulsion  is  mu- 
tual, the  point  is  pushed 
back  with  the  same  force 
with  which  these  ions  are 
pushed  forward  ;  hence  the 
rotation.  The  repelled  ions 
in  their  turn  drag  the  air  with  them  in  their  forward  motions 
and  thus  produce  the  "  electric  wind,"  which  may  be  detected 
easily  by  the  hand  or  by  a  candle  flame  (Fig.  233). 

292.  Lightning  and  lightning  rods.  It  was  in  1752  that 
Franklin  (see  opposite  p.  230),  during  a  thunderstorm,  sent 
up  his  historic  kite  (see  opposite  p.  231).  This  kite  was  pro- 
vided with  a  pointed  wire  at  the  top.  As  soon  as  the  hempen 
kite-string  had  become  wet  he  succeeded  in  drawing  ordinary 
electric  sparks  from  a  key  attached  to  the  lower  end.  This 
experiment  demonstrated  for  the  first  time  that  thunderclouds 
carry  ordinary  electrical  charges  which  may  be  drawn  from 
them  by  points,  just  as  the  charge  was  drawn  from  the  tassel 
in  the  experiment  of  §  290.  It  also  showed  that  lightning  is 
nothing  but  a  huge  electric  spark.  Franklin  applied  this  dis- 
covery in  the  invention  of  the  lightning  rod.  The  way  in  which 
the  rod  discharges  the  cloud  and  protects  the  building  is  as 
follows :  As  the  charged  cloud  approaches  the  building  it 
induces  an  opposite  charge  in  the  rod.  This  induced  charge 
escapes  rapidly  and  quietly  from  the  sharp  point  in  the  manner 
explained  above  and  thus  neutralizes  the  charge  of  the  cloud. 

To  illustrate,  let  a  metal  plate  C  (Fig.  234)  be  supported  above  a 
metal  ball  E,  and  let  C  and  E  be  attached  to  the  two  knobs  of  an  electri- 
cal machine.  When  the  machine  is  started,  sparks  will  pass  from  C  to  E. 


POTENTIAL  AND  CAPACITY 


237 


But  if  a  point  p  is  connected  to  E,  the  sparking  will  cease ;  that  is,  the 
point  will  protect  E  from  the  discharges,  even  though  the  distance  Cp 
be  considerably  greater  than  CE. 

The  lower  end  of  a  lightning  rod  should  be  buried  deep 
enough  so  that  it  will  always  be  surrounded  by  moist  earth, 
since  dry  earth  is  a  poor  conductor.  It  will  be  seen,  therefore, 
that  lightning  rods  protect 
buildings  not  because  they 
conduct  the  lightning  to  earth, 
but  because  they  prevent  the 
formation  of  powerful  charges 
in  the  neighborhood  of  the 
buildings  on  which  they  are 
placed. 

Flashes  of  lightning  over  a 
mile  long  have  frequently  been  observed.  Thunder  is  due  to 
the  violent  expansion  of  heated  air  along  the  path  of  discharge. 
The  roll  of  thunder  is  due  to  reflections  from  clouds,  hills,  etc.* 


FIG.  234.    Illustrating  the  action  of 
a  lightning  rod 


POTENTIAL  AND  CAPACITY 

293.  Potential  difference.  There  is  a  very  instructive  anal- 
ogy between  the  use  of  the  word  "  potential "  in  electricity 
and  "  pressure  "  in  hydrostatics.  For  ex- 
ample, if  water  will  flow  from  tank  A  to 
tank  B  through  the  connecting  pipe  R 
(Fig.  235),  we  infer  that  the  hydrostatic 
pressure  at  a  must  be  greater  than  that 
at  J,  and  we  attribute  the  flow  directly 
to  this  difference  in  pressure.  In  exactly 
the  same  way,  if,  when  two  bodies  A  and  B  (Fig.  236)  are 
connected  by  a  conducting  wire  r,  a  charge  of  -f-  electricity 


R 


*  A  laboratory  exercise  on  static  electrical  effects  should  follow  the  discus- 
sion of  this  section.  See,  for  example,  Experiment  27  of  the  authors'  Manual. 


238  STATIC  ELECTRICITY 

is  found  to  pass  from  A  to  B  (that  is,  if  electrons  are  found 
to  pass  from  B  to  A)  we  say  that  the  electrical  potential  is 
higher  at  A  than  at  B,  and  we  assign  this  difference  of  poten- 
tial as  the  cause  of  the  flow.*  Thus,  just  as  water  tends  to 
flow  from  points  of  higher  hydrostatic  pressure  to  points  of 
lower  hydrostatic  pressure,  so  elec-  ^_^  ^_^ 

tricity  tends  to  flow  from  points  of     (• <O ( B  j 

higher  electrical  pressure,  or  poten- 

, . &,  .    ,        f   ,  ,    .     ,      FIG.  236.    Illustrating  electri- 

tial,  to  points  of  lower  electrical  cal  pressure 

pressure,  or  potential. 

Again,  if  water  is  not  continuously  supplied  to  one  of  the 
tanks  A  or  B  of  Fig.  235,  we  know  that  the  pressures  at 
a  and  b  must  soon  become  the  same.  Similarly,  if  no  elec- 
tricity is  supplied  to  the  bodies  A  and  B  of  Fig.  236,  their 
potentials  very  quickly  become  the  same.  In  other  words, 
all  points  on  a  system  of  connected  conductors  in  which  the 
electricity  is  in  a  stationary,  or  static,  condition  are  at  the  same 
potential.  This  result  follows  at  once  from  the  fact  of  mobility 
of  electric  charges  through  conductors. 

But  if  water  is  continuously  poured  into  A  and  removed 
from  B  (Fig.  235),  the  pressure  at  a  will  remain  permanently 
above  the  pressure  at  b,  and  a  continuous  flow  of  water  will 
take  place  through  R.  So,  if  A  (Fig.  236)  is  connected  with  an 
electrical  machine  and  B  to  earth,  a  permanent  potential  differ- 
ence will  exist  between  A  and  B,  and  a  continuous  current  of 
electricity  will  flow  through  r.  Difference  in  potential  is 
commonly  denoted  simply  by  the  letters  P.  D.  (Potential 
Difference). 

*  Franklin  thought  that  it  was  the  positive  electricity  which  moved  through 
a  conductor,  while  he  conceived  the  negative  as  inseparably  associated  with 
the  atoms.  Hence  it  became  a  universally  recognized  convention  to  regard 
electricity  as  moving  through  a  conductor  in  the  direction  in  which  a  -f  charge 
would  have  to  move  in  order  to  produce  the  observed  effect.  It  is  not  de- 
sirable to  attempt  to  change  this  convention  now,  even  though  the  electron 
theory  has  exactly  inverted  the  roles  of  the  +  and  —  charges. 


POTENTIAL  AND  CAPACITY 


239 


294.  Some  methods  of  measuring  potentials.  The  simplest 
and  most  direct  way  of  measuring  the  potential  difference  be- 
tween two  bodies  is  to  connect  one  to  the  knob,  the  other  to 
the  conducting  case,*  of  an  electroscope.  The  amount  of 
separation  of  the  gold  leaves  is  a  measure  of  the  P.D.  between 
the  bodies.  The  unit  in  which  P.D.  is  usually  expressed  is 
called  the  volt.  It  will  be  accurately  denned  in  §  334.  It  will 
be  sufficient  here  to  say  that  it  is  approximately  equal  to  the 
electrical  pressure  between  the  ends  of  copper  and  zinc  strips 
when  dipped  in  dilute  sulphuric  acid 
or  to  two  thirds  of  the  electrical  pres- 
sure between  the  zinc  and  carbon 
terminals  of  the  familiar  dry  cell. 

Since  the  earth  is,  on  the  whole, 
a  good  conductor,  its  potential  is 
everywhere  the  same  (§  293) ;  hence 
it  makes  a  convenient  standard  of 
reference  in  potential  measurements. 
To  find  the  potential  of  a  body  rela- 
tive to  that  of  the  earth,  we  connect 
the  outer  case  of  the  electroscope  to 
the  earth  by  means  of  a  wire,  and 
connect  the  body  to  the  knob.  If  the 
electroscope  is  calibrated  in  volts, 
its  reading  gives  the  P.D.  between 
the  body  and  the  earth.  Such  cali- 
brated electroscopes  are  called  electrostatic  voltmeters.  They 
are  the  simplest  and  in  many  respects  the  most  satisfactory 
forms  of  voltmeters  to  be  had.  Their  use,  both  in  laboratories 


FIG.  237.    Electrostatic 
voltmeter 


*  If  the  case  is  of  glass,  it  should  always  be  made  conducting  by  pasting 
tin-foil  strips  on  the  inside  of  the  jar  opposite  the  leaves  and  extending  these 
strips  over  the  edge  of  the  jar  and  down  on  the  outside  to  the  conducting 
support  on  which  the  electroscope  rests.  The  object  of  this  is  to  maintain 
the  walls  always  at  the  potential  of  the  earth. 


240 


STATIC  ELECTRICITY 


and  in  electrical  power  plants,  is  rapidly  increasing.  They 
can  be  made  to  measure  a  P.D.  as  small  as  l  *QQ  volt  and  as 
large  as  200,000  volts.  Fig.  237  shows  one  of  the  simpler 
forms.  The  outer  case  is  of  metal  and  is  connected  to  earth 
at  the  point  a.  The  body  whose  potential  is  sought  is  con- 
nected to  the  knob  b.  This  is  in  metallic  contact  with  the 
light  aluminium  vane  c,  which  takes  the  place  of  the  gold  leaf. 
A  very  convenient  way  of  measuring  a  large  P.D.  without 
a  voltmeter  is  to  measure  the  length  of  the  spark  which  will 
pass  between  the  two  bodies  whose  P.D.  is  sought.  The  P.D. 
is  roughly  proportional  to  spark  length,  each  centimeter  of 
spark  length  representing  a  P.D.  of  about  30,000  volts  if  the 
electrodes  are  large  compared  to  their  distance  apart. 

295.  Condensers.  Let  a  metal  plate  A  be  mounted  on  an  insulating 
base  and  connected  with  an  electroscope,  as  in  Fig.  238.  Let  a  second 
plate  B  be  simi-  A  R 

larly  mounted  and 
connected  to  the 
earth  by  a  conduct- 
ing wire.  Let  A  be 
charged  and  the 
deflection  of  the 
gold  leaves  noted. 
If  now  we  push  B 
toward  A,  we  shall  observe  that,  as  it  comes  near,  the  leaves  begin  to 
fall  together,  showing  that  the  potential  of  A  is  diminished  by  the 
presence  of  B,  although  the  quantity  of  electricity  on  A  has  remained 
unchanged.  If  we  convey  additional  —  charges  to  A  with  the  aid  of  a 
proof  plane,  we  shall  find  that  many  times  the  original  amount  of  elec- 
tricity may  now  be  put  on  A  before  the  leaves  return  to  their  original 
divergence,  that  is,  before  the  body  regains  its  original  potential. 

We  say,  therefore,  that  the  capacity  of  A  for  holding  elec- 
tricity has  been  very  greatly  increased  by  bringing  near  it 
another  conductor  which  is  connected  to  earth.  It  is  evident 
from  this  statement  that  we  measure  the  capacity  of  a  body  by 
the  amount  of  electricity  which  must  be  put  upon  it  to  raise  it  to 


FIG.  238.   The  principle  of  the  condenser 


COUNT  ALESSANDRO  VOLTA  (1745-1827) 

Great  Italian  physicist,  professor  at  Como  and  at  Pavia ;  inventor 
of  the  electroscope,  the  electrophorus,  the  condenser,  and  the 
yoltaic  pile  (a  form  of  galvanic  cell) ;  first  measured  the  potential 
differences  arising  from  the  contact  of  dissimilar  substances; 
ennobled  by  Napoleon  for  his  scientific  services;  the  volt,  the 
practical  unit  of  potential  difference,  is  named  in  Ms  honor 


A  MODERN  HIGH-TENSION  TOWER  ON  THE  SOUTHERN  CALIFORNIA  EDISON 
COMPANY'S  BIG  CREEK  LINE 

These  wires  carry  an  alternating  current  having  a  potential  of  150,000  volts.  The 
current  is  generated  hy  four  17,500-kilowatt  dynamos  driven  hy  8  Pelton  water- 
wheels  operating  under  a  head  of  1900  feet  and  developing  a  horse  power  of  100,000. 
Even  in  wet  weather  the  under  surfaces  of  the  series  of  nine  petticoat  insulators 
from  which  each  wire  is  hung  remain  sufficiently  dry  to  prevent  large  leakage 
losses.  The  wires  are  spaced  16  feet  apart 


POTENTIAL  AND  CAPACITY  241 

a  given  potential.  The  explanation  of  the  increase  in  capacity 
in  this  case  is  obvious.  As  soon  as  B  was  brought  near  to  A 
it  became  charged,  by  induction,  with  electricity  of  opposite 
sign  to  J,  the  electricity  of  like  sign  to  A  being  driven  off  to 
earth  through  the  connecting  wire.  The  attraction  between 
these  opposite  charges  on  A  and  B  drew  the  electricity  on  A 
to  the  face  nearest  to  B  and  removed  it  from  the  more  remote 
parts  of  A,  so  that  it  became  possible  to  put  a  very  much 
larger  charge  on  A  before  the  tendency  of  the  electricity  on  A 
to  pass  over  to  the  electroscope  became  as  great  as  it  was  at 
first,  that  is,  before  the  potential  of  A  rose  to  its  initial  value. 
In  such  a  condition  the  electricity  on  A  is  said  to  be  bound 
by  the  opposite  electricity  on  B. 

An  arrangement  of  this  sort  consisting  of  two  conductors  sepa- 
rated by  a  nonconductor  is  called  a  condenser.  If  the  conducting 
plates  are  very  close  together  and  one  of  them  grounded,  the 
capacity  of  the  system  may  be  thou- 
sands of  times  as  great  as  that  of  one 
of  the  plates  alone. 

296.  The  Leyden  jar.  The  most  com- 
mon form  of  condenser  is  a  glass  jar 
coated  part  way  to  the  top  inside  and 
outside  with  tin  foil  (Fig.  239).  The 

inside  coating-  is  connected  by  a  chain  to 

*  J  .        FIG.  239.  The  Leyden  jar 

the  knob,  while  the  outside  coating  is 

connected  to  earth.  Condensers  of  this  sort  first  came  into 
use  in  Leyden,  Holland,  in  1745.  Hence  they  are  now  called 
Leyden  jars. 

To  charge  a  Leyden  jar  the  outer  coating  is  held  in  the  hand  while 
the  knob  is  brought  into  contact  with  one  terminal  of  an  electrical 
machine,  —  for  example,  the  negative.  As  fast  as  electrons  pass  to  the 
knob  they  spread  to  the  inner  coat  of  the  jar,  where  they  repel  electrons 
from  the  outer  coat  to  the  earth,  thus  leaving  it  positively  charged.  If 
the  inner  and  outer  coatings  are  now  connected  by  a  discharging  rod, 


242 


STATIC  ELECTRICITY 


as  in  Fig.  239,  a  powerful  spark  will  be  produced.  This  spark  is  due  to 
the  rush  of  electrons  from  the  —  coat  to  the  +  coat.  Let  a  charged 
jar  be  placed  on  a  glass  plate  so  as  to  insulate  the  outer  coat.  Let  the 
knob  be  touched  with  the  finger;  no  appreciable  discharge  will  be 
noticed.  Let  the  outer  coat  be  in  turn  touched  with  the  finger ;  again 
no  appreciable  discharge  will  appear.  But  if  the  inner  and  outer  coatings 
are  connected  with  the  discharger,  a  powerful  spark  will  pass. 

The  experiment  shows  that  it  is  impossible  to  discharge 
one  side  of  the  jar  alone,  for  practically  all  of  the  charge  is 
bound  by  the  opposite  charge  on  the  other  coat.  The  full 
discharge  can  therefore  occur  only  when  the  inner  and  outer 
coats  are  connected. 

Leyden  jars  and  other  forms  of  condensers  are  of  great 
practical  use.  They  are  used,  for  instance,  in  certain  systems 
of  telephony  and  telegraphy,  in  wireless 
communication,  and  in  electrostatic  ma- 
chines and  induction  coils. 


FIG.  240.   The  elec- 
trophorus 


297.  The  electrophorus.  The  electrophorus 

is  a  simple  electrical  generator  which  illustrates 
well  the  principle  underlying  the  action  of  all 
electrostatic  machines.  All  such  machines  gen- 
erate electricity  primarily  by  induction,  not  by 
friction.  B  (Fig.  240)  is  a  hard-rubber  plate 
which  is  first  charged  by  rubbing  it  with  fur  or 
flannel.  A  is  a  metal  plate  provided  with  an  insulating  handle.  When 
the  plate  A  is  placed  upon  B,  touched  with  the  finger,  and  then  removed, 
it  is  found  possible  to  draw  a  spark  from  it,  which  in  dry  weather  may 
be  a  quarter  of  an  inch  or  more  in  length.  The  process  may  be  repeated 
an  indefinite  number  of  times  without  producing  any  diminution  in  the 
size  of  the  spark  which  may  be  drawn  from  A. 

If  the  sign  of  the  charge  on  A  is  tested  by  means  of  an 
electroscope,  it  will  be  found  to  be  positive.  This  proves 
that  A  has  been  charged  by  induction,  not  by  contact  with  B, 
for  it  is  to  be  remembered  that  the  latter  is  charged  nega- 
tively. The  reason  for  this  is  that  even  when  A  rests  upon 
B  it  is  in  reality  separated  from  it,  at  all  but  a  very  few 


POTENTIAL  AND  CAPACITY  243 

points,  by  an  insulating  layer  of  air ;  and  since  B  is  a  non- 
conductor, its  charge  cannot  pass  off  appreciably  through 
these  few  points  of  contact.  It  simply  repels  negative  elec- 
trons to  the  top  side  of  the  metal  plate  A,  and  thus  charges 
positively  the  lower  side.  The  electrons  pass  off  to  earth 
when  the  plate  is  touched  with  the  finger.  Hence,  when  the 
finger  is  removed  and  A  lifted,  it  possesses  a  strong  positive 
charge.  Every  commercial  electrostatic  machine  is  simply  a 
continuously  acting  electrophorus  which  generates  electricity 
by  induction,  not  by  friction. 

QUESTIONS  AND  PROBLEMS 

1.  If  you  set  a  charged  Ley  den  jar  on  a  cake  of  paraffin,  why  can 
you  not  discharge  it  by  touching  one  of  the  coatings  ? 

2.  Will  a  solid   sphere  hold  a  larger  charge  of  electricity  than  a 
hollow  one  of  the  same  diameter? 

3.  Why  cannot  a  Leyden  jar  be  appreciably  charged  if  the  outer  coat 
is  insulated  ? 

4.  With  a  stick  of  sealing  wax  and  a  piece  of  flannel,  in  what  two 
ways  could  you  give  a  positive  charge  to  an  insulated  body? 

5.  Explain,  using  a  set  of  drawings,  the  charging  of  the  cover  of  an 
electrophorus. 

6.  Represent  by  a  drawing  the  electrical  condition  of  a  tower  just 
before  it  is  struck  by  lightning,  assuming  the  cloud  at  this  particular 
time  to  be  powerfully  charged  with  +  electricity. 

7.  When  a  negatively  electrified  cloud  passes  over  a  house  provided 
with  a  lightning  rod,  the  rod  discharges  positive  electricity  into  the 
cloud.    Explain. 


CHAPTER  XIV 


ELECTRICITY  IN  MOTION  * 
DETECTION  OF  ELECTRIC  CURRENTS 
298.  Electricity  in  motion  produces  a  magnetic  effect.    Let  a 

powerfully  charged  Leyden  jar  be  discharged  through  a  coil  which  sur- 
rounds an  unmagnetized  knitting  needle,  insulated  by  a  glass  tube,  in 
the  manner  shown  in  Fig.  241,  the  compass  needle  being  at  rest  in  the 
position  shown.    After  the  discharge  the  knitting 
needle  will  be  found  to  be  distinctly  magnetized. 
If  the  sign  of  the  charge  on  the  jar  is  reversed, 
the  direction  of  deflection  and 
the  poles  will  in  general  be 
reversed. 

The  experiment  shows 
that  there  is  a  definite 
connection  between  elec- 
tricity and  magnetism. 
Just  what  this  connection  is  we  do  not  yet  know  with  cer- 
tainty, but  we  do  know  that  magnetic  effects  are  always  ob- 
servable near  the  path  of  a  moving  electrical  charge,  while 
no  such  effects  can  ever  be  observed  near  a  charge  at  rest. 

To  prove  that  a  charge  at  rest  does  not  produce  a  magnetic  effect, 
let  a  charged  body  be  brought  near  a  compass  needle.  It  will  attract 
either  end  of  the  needle  with  equal  readiness.  While  the  needle  is 
deflected,  insert  between  it  and  the  charge  a  sheet  of  zinc,  aluminium, 
brass,  or  copper.  This  will  act  as  an  electric  screen  and  will  therefore 
cut  off  all  effect  of  the  charge.  The  compass  needle  will  at  once  swing 
to  its  north-and-south  position. 


FIG.  241.    Magnetic  effect  of  an  electric 
current  produced  from  a  static  charge 


*  This  chapter  should  be  accompanied  or,  better,  preceded  by  laboratory 
experiments  on  the  simple  cell  and  on  the  magnetic  effects  of  a  current.  See, 
for  example,  Experiments  28,  29,  and  30  of  the  authors'  Manual. 

244 


DETECTION  OF  ELECTRIC  CURRENTS          245 

Let  the  compass  needle  be  deflected  by  a  bar  magnet,  and  let  the 
screen  be  inserted  again  The  sheet  of  metal  does  not  cut  off  the 
magnetic  forces  in  the  slightest  degree. 

The  fact  that  an  electric  charge  exerts  no  magnetic  force  is  shown, 
then,  both  by  the  fact  that  it  attracts  either  end  of  the  compass  needle 
with  equal  readiness  and  by  the  fact  that  the  screen  cuts  off  its  action 
completely,  while  the  same  screen  does  not  have  any  effect  in  cutting 
off  the  magnetic  force. 

An  electrical  charge  in  motion  is  called  an  electric  current, 
and  its  presence  is  most  commonly  detected  by  the  magnetic 
effect  which  it  produces.  A  current  of  electricity  is  now  con- 
sidered to  be  a  stream  of  negative  electrons  (see  §  293). 

299.  The  galvanic  cell.  When  a  Leyden  jar  is  discharged, 
only  a  very  small  quantity  of  electricity  passes  through  the 
connecting  wires,  since  the  current  lasts  for  but  a  small  frac- 
tion of  a  second.  If  we  could  keep  a  current  flowing  continu- 
ously through  the  wire,  we  should  expect  the  magnetic  effect 
to  be  much  more  pronounced.  It  was  in  1786 
that  Galvani,  an  Italian  anatomist  at  the  Uni- 
versity of  Bologna,  accidentally  discovered  that 
there  is  a  chemical  method  for  producing  such 
a  continuous  current.  His  discovery  was  not 
understood,  however,  until  Volta  (see  opposite 

p.  240X  while  endeavoring*  to  throw  liofht  upon     FIG. 242.  Sim- 

ple  voltaic  cell 
it,  in  1800  invented  an  arrangement  which  is 

now  known  sometimes  as  the  voltaic  and  sometimes  as  the 
galvanic  cell.  This  consists,  in  its  simplest  form,  of  a  strip  of 
copper  and  a  strip  of  zinc  immersed  in  dilute  sulphuric  acid 
(Fig.  242). 

Let  the  terminals  of  such  a  cell  be  connected  for  a  few  seconds  to  the 
ends  of  the  coil  of  Fig.  241  when  an  unmagnetized  needle  lies  within 
the  glass  tube.  The  needle  will  be  found  to  have  become  magnetized 
much  more  strongly  than  before.  Again,  let  the  wire  which  connects 
the  terminals  of  the  cell  be  held  above  a  magnetic  needle,  as  in  Fig.  243 ; 
the  needle  will  be  strongly  deflected 


246  ELECTRICITY  IN  MOTION 

Evidently,  then,  the  wire  which  connects  the  terminals  of  a 
galvanic  cell  carries  a  current  of  electricity.    Historically  the 
second  of  these  experiments,  per- 
formed by  the  Danish  physicist 
Oersted  (see  on  opposite  page) 
in  1820,  preceded  the  discovery 
of  the  magnetizing  effects  of  cur- 
rents upon  needles.   It  created  a      FlG  243    oersted's  experiment 
great  deal  of  excitement  at  the 

time,  because  it  was  the  first  clue   which  had  been  found 
to  a  relationship  between  electricity  and  magnetism. 

300.  Plates  of  a  galvanic  cell  are  electrically  charged.  Since 
an  electric  current  flows  through  a  wire  as  soon  as  it  is  touched 
to  the  zinc  and  copper  strips  of  a  galvanic  cell,  we  at  once 
infer  that  the  terminals  of  such  a  cell  are  electrically  charged 
before  they  are  connected.  That  this  is  indeed  the  case  may 
be  shown  as  follows : 

Let  a  metal  plate  A  (Fig.  244),  covered  with  shellac  on  its  lower  side 
and  provided  with  an  insulating  handle,  be  placed  upon  a  similar  plate 
B  which  is  in  contact  with  the  knob  of  an  electroscope.  Let  the  copper 
plate  of  a  galvanic  cell  be  connected  with  A  and  the  zinc  plate  with  Bf 
as  in  Fig.  244.  Then  let  the  connecting  wires  be  removed  and  the 
plate  A  lifted  away  from  B.  The  opposite  electrical  charges  which  were 
bound  by  their  mutual  attractions  to  the  adjacent  faces  of  A  and  B,  so- 
long,  as  these  faces  were  separated  only  by  the  thin  coat  of  shellac,  are 
freed  as  soon  as  A  is  lifted,  and  hence  part  of  the  charge  on  B  passes 
to  the  leaves  of  the  electroscope.  These  leaves  will  indeed  be  seen  to 
diverge.  If  an  ebonite  rod  which  has  been  rubbed  with  flannel  or  cat's  fur 
is  brought  near  the  electroscope,  the  leaves  will  diverge  still  farther,  thus 
showing  that  the  zinc  plate  of  the  galvanic  cell  is  negatively  charged.*  If 
the  experiment  is  repeated  with  the  copper  plate  in  contact  with  B  and  the 
zinc  in  contact  with  A,  the  leaves  will  be  found  to  be  positively  charged. 

*  If  the  deflection  of  the  gold  leaves  is  too  small  for  purposes  of  demon- 
stration, let  a  battery  of  from  five  to  ten  cells  be  used  instead  of  the  single 
cell.  If,  however,  the  plates  A  and  B  are  three  or  four  inches  in  diameter, 
and  if  their  surfaces  are  very  flat,  a  single  cell  is  sufficient. 


HANS  CHRISTIAN  OERSTED 

(1777-1851) 

The  discoverer  of  the  connection 
'between  electricity  and  magnetism 
was  a  Dane  and  a  professor  at  the 
University  of  Copenhagen.  His 
famous  experiment  made  in  1820 
stimulated  the  researches  which 
led  to  the  modern  industrial  devel- 
opments of  electricity 


JOSEPH  HENRY  (1797-1878) 

Born  in  Albany,  New  York ;  taught 
physics  and  mathematics  in  Albany 
Academy  and  Princeton  College. 
He  invented  the  electromagnet 
(1828),  discovered  the  oscillatory 
nature  of  the  electric  spark  (1842) 
by  magnetizing  needles  in  the 
manner  described  on  page  244,  and 
made  the  first  experiments  in  self- 
induction  (1832).  He  was  the  first 
secretary  of  the  Smithsonian  Insti- 
tution, and  the  organizer  of  the 
Weather  Bureau 


ELECTROMAGNETS 

This  page  shows  in  the  upper  right-hand  corner  a  photograph  of  the  first  electro- 
magnet. It  was  constructed  at  Princeton  in  1828  by  Henry.  He  wound  the  arms 
of  a  U-shaped  piece  of  iron  with  several  layers  of  wire  insulated  by  wrapping 
around  it  strips  of  silk.  The  main  illustration  is  a  huge  modern  lifting  magnet 
which  itself  weighs  8720  pounds,  is  5  feet  2  inches  in  diameter,  and  can  lift  a 
single  flat  piece  of  iron  weighing  70,000  pounds.  It  has  118,000  ampere  turns,  and 
carries  84  amperes  at  220  volts.  The  coil  is  built  up  of  several  pancakes  of  cop- 
per straps,  the  turns  of  strap  being  insulated  from  one  another  by  asbestos  ribbon 
wound  between  them.  The  magnet  is  loading  a  freight  car  with  pig  iron,  of  which 
its  average  lift  is  4000  pounds 


DETECTION  OF  ELECTRIC  CURRENTS          247 

The  terminals  of  a  galvanic  cell  therefore  carry  positive 
and  negative  charges  just  as  do  the  terminals  of  an  electrical 
machine  in  operation.  The  +  charge  is 
always  found  upon  the  copper  and  the  - 
charge  upon  the  zinc.  The  source  of 
these  charges  is  the  chemical  action 
which  takes  place  within  the  cell.  When 
these  terminals  are  connected  by  a  con- 
ductor, a  current  flows  through  the  latter 

just  as  in  the  case  of  the  electrical  ma-       FlG-  244-    Showing 
,  .  ,    ..    .      .,  .  charges  on  plates  of 

chine;  and  it  is  the  universal  custom  to  a  voltaic  cell 

consider  that  it  flows  from  positive  to  neg- 
ative (see  §  293  and  footnote),  that  is,  from  copper  to  zinc. 

301.  Comparison  of  a  galvanic  cell  and  a  static  machine.  If 
one  of  the  terminals  of  a  galvanic  cell  is  touched  directly  to 
the  knob  of  a  gold-leaf  electroscope,  without  the  use  of  the 
condenser  plates  A  and  B  of  Fig.  244,  no  divergence  of  the 
leaves  will  be  detected ;  but  if  one  knob  of  a  static  machine 
in  operation  were  so  touched,  the  leaves  would  probably  be 
torn  apart  by  the  violence  of  the  divergence.  Since  we  have 
seen  in  §  294  that  the  divergence  of  the  gold  leaves  is  a  meas- 
ure of  the  potential  of  the  body  to  which  they  are  connected, 
we  learn  from  this  experiment  that  the  chemical  actions  in  the 
galvanic  cell  are  able  to  produce  between  its  terminals  but  a 
very  small  potential  difference  in  comparison  with  that  pro- 
duced by  the  static  machine  between  its  terminals.  As  a  matter 
of  fact  the  potential  difference  between  the  terminals  of  the 
cell  is  about  one  volt,  while  that  between  the  knobs  of  the 
electrical  machine  may  be  as  much  as  200,000  volts. 

But  if  the  knobs  of  the  static  machine  are  connected  to  the 
ends  of  the  wire  of  Fig.  243,  and  the  machine  operated,  the  cur- 
rent sent  through  the  wire  will  not  be  large  enough  to  produce 
any  appreciable  effect  upon  the  needle.  Since  under  these  same 
circumstances  the  galvanic  cell  produced  a  very  large  effect 


248  ELECTKICITY  IN  MOTION 

upon  the  needle,  we  learn  that  although  the  cell  develops  a  very 
small  P.D.  between  its  terminals,  it  nevertheless  sends  through 
the  connecting  wire  very  much  more  electricity  per  second 
than  the  static  machine  is  able  to  send.  This  is  because  the 
chemical  action  of  the  cell  is  able  to  recharge  the  plates  to 
their  small  P.D.  practically  as  fast  as  they  are  discharged 
through  the  wire,  whereas  the  static  machine  requires  a  rela- 
tively long  time  to  recharge  its  terminals  to  their  high  P.  D. 
after  they  have  once  been  discharged. 

QUESTIONS  AND  PROBLEMS 

1.  Under  what  conditions  will  an  electric  charge  produce  a  magnetic 
effect? 

2.  How  can  you  test  whether  or  not  a  current  is  flowing  in  a  wire  ? 

3.  How  does  the  current  delivered  by  a  cell  differ  from  that  delivered 
by  a  static  machine  ? 

4.  Mention  three  respects  in  which  the  behavior  of  magnets  is  similar 
to  that  of  electric  charges ;  two  respects  in  which  it  is  different. 

CHEMICAL  EFFECTS  OF  THE  CURRENT  ;  ELECTROLYSIS  * 

302.  Electrolysis.  Let  two  platinum  electrodes  be  dipped  into  a 
solution  of  dilute  sulphuric  acid,  and  let  the  terminals  of  a  battery 
producing  a  pressure  of  10  volts  or  more  be  applied  to  these  electrodes. 
Oxygen  gas  is  found  to  be  given  off  at  the  electrode  at  which  the  cur- 
rent enters  the  solution,  called  the  anode,  while  hydrogen  is  given  off 
at  the  electrode  at  which  the  current  leaves  the  solution,  called  the 
cathode.  These  gases  may  be  collected  in  test  tubes  in  the  manner 
shown  in  Fig.  245. 

In  accordance  with  the  theory  now  in  vogue  among  physi- 
cists and  chemists,  when  sulphuric  acid  is  mixed  with  water 
so  as  to  form  a  dilute  solution,  the  H2SO4  molecules  split 
up  into  three  electrically  charged  parts,  called  ions,  the  two 

*  This  subject  should  be  accompanied  or  followed  by  a  laboratory  experi- 
ment on  electrolysis  and  the  principle  of  the  storage  battery.  See,  four 
example,  Experiment  35  of  the  authors'  Manual. 


CHEMICAL  EFFECTS;  ELECTROLYSIS 


249 


FIG.  245.    Electrolysis 
of  water 


hydrogen  ions  each  carrying  a  positive  charge  and  the  SO4  ion 
a  double  negative  charge  (Fig.  246).  This  phenomenon  is 
known  as  dissociation.  The  solution  as 
a  whole  is  neutral ;  that  is,  it  is  un- 
charged, because  it  contains  just  as  many 
positive  as  negative  charges. 

As  soon  as  an  electrical  field  is  estab- 
lished in  the  solution  by  connecting  the 
electrodes  to  the  positive  and  negative 
terminals  of  a  battery,  the  hydrogen  ions 
begin  to  migrate  toward  the  negative  elec- 
trode (that  is,  the  cathode)  and  there,  after  giving  up  their 
charges,  unite  to  form  molecules  of  hydrogen  gas  (Fig.  245). 
On  the  other  hand,  the  negative 
SO4  ions  migrate  to  the  positive 
electrode  (that  is,  the  anode), 
where  they  give  up  their  charges 
to  it,  and   then    act  upon  the 
water     (H2O),    thus     forming 
H2SO4   and  liberating  oxygen. 

If  the  volumes  of  Iwdrogen 

J        &  FIG.  246.   Showing  dissociation  of 

and  of   oxygen   are    measured,     sulphuric-acid  molecules  in  water 
the  hydrogen  is  found  to  occupy 

in  every  case  just  twice  the  volume  occupied  by  the  oxygen. 
This  is,  indeed,  one  of  the  reasons  for  believing  that  a  molecule 
of  water  consists  of  two  atoms  of  hydrogen  and  one  of  oxygen. 
303.  Electroplating.  If  the  solution,  instead  of  being  sul- 
phuric acid,  had  been  one  of  copper  sulphate  (CuSO4),  the 
results  would  have  been  precisely  the  same  in  every  respect, 
except  that,  since  the  hydrogen  ions  in  the  solution  are  now 
replaced  by  copper  ions,  the  substance  deposited  on  the  cathode 
is  pure  copper  instead  of  hydrogen.  This  is  the  principle 
involved  in  electroplating  of  all  kinds.  In  commercial  work 
the  positive  plate,  that  is,  the  plate  at  which  the  current 


250 


ELECTRICITY  IN  MOTION 


X 


FIG.  247.    A  simple  electro- 
plating bath 


enters  the  bath,  is  always  made  from  the  same  metal  as  that 
which  is  to  be  deposited  from  the  solution,  for  in  this  case 
the  SO4  or  other  negative  ions  dissolve  this  plate  as  fast  as 
the  metal  ions  are  deposited  upon 
the  other.  The  strength  of  the  solu- 
tion, therefore,  remains  unchanged. 
In  effect,  the  metal  is  simply  taken 
from  one  plate  and  deposited  on  the 
other.  Fig.  247  represents  a  simple 
form  of  silver-plating  bath.  The 
anode  A  is  of  pure  silver.  The 
spoon  to  be  plated  is  the  cathode  K.  In  practice  the  articles  to 
be  plated  are  often  suspended  from  a  central  rod  (Fig.  248). 
while  on  both  sides  about  the  articles  are  the  suspended 
anodes.  This  arrangement  gives 
a  more  even  deposit  of  metal. 
In  silver  plating  the  solution 
consists  of  500  grams  of  potas- 
sium cyanide  and  250  grams  of 
silver  cyanide  in  10  liters  of 
water. 


FIG.  248.    Electroplating  bath 


304.  Electrotyping.  In  the  process  of  electrotyping,  the  page 
is  first  set  up  in  the  form  of  common  type.  A  mold  is  then 
taken  in  wax  or  gutta-percha.  This  mold  is  then  coated  with 
powdered  graphite  to  render  it  a  conductor,  after  which  it  is 
ready  to  be  suspended  as  the  cathode  in  a  copper-plating  bath, 
the  anode  being  a  plate  of  pure  copper  and  the  liquid  a  solu- 
tion of  copper  sulphate.  When  a  sheet  of  copper  as  thick  as 
a  visiting  card  has  been  deposited  on  the  mold,  the  latter  is 
removed  and  the  wax  replaced  by  a  type-metal  backing,  to 
give  rigidity  to  the  copper  films.  From  such  a  plate  as  many 
as  a  hundred  thousand  impressions  may  be  made.  Nearly 
all  books  which  run  through  large  editions  are  printed  from 
such  electrotypes. 


CHEMICAL  EFFECTS;  ELECTEOLYSIS  251 

305.  Legal  units  of  current  and  quantity.  In  1834  Faraday 
(see  opposite  p.  290)  found  that  a  given  current  of  elec- 
tricity flowing  for  a  given  time  always  deposits  the  same 
amount  of  a  given  element  from  a  solution,  whatever  be  the 
nature  of  the  solution  which  contains  the  element.  For  ex- 
ample, one  ampere,  the  unit  of  current,  always  deposits  in  an 
hour  4.025  grams  of  silver,  whether  the  electrolyte  is  silver 
nitrate,  silver  cyanide,  or  any  other  silver  compound.  Simi- 
larly, an  ampere  will  deposit  in  an  hour  1.181  grams  of  copper, 
1.203  grams  of  zinc,  etc.  Faraday  further  found  that  the 
amount  of  metal  deposited  in  a  given  cell  depended  solely 
on  the  product  of  the  current  strength  by  the  time,  that  is,  on 
the  quantity  of  electricity  which  had  passed  through  the  cell. 
These  facts  are  made  the  basis  of  the  legal  definitions  of 
current  and  quantity,  thus : 

The  unit  of  quantity,  called  the  coulomb,  is  the  quantity  of 
electricity  required  to  deposit  .001118  gram  of  silver. 

The  unit  of  current,  the  ampere,  is  the  current  which  will 
deposit  .001118  gram  of  silver  in  one  second. 

QUESTIONS  AND  PROBLEMS 

1.  What  was  the  strength  of  a  current  that  deposited  11.84  g.  of 
copper  in  30  min.  ? 

2.  How  long  will  it  take  a  current  of  1  ampere  to  deposit  1  g.  of 
silver  from  a  solution  of  silver  nitrate  ? 

3.  If  the  same  current  used  in  Problem  2  were  led  through  a  solution 
containing  a  zinc  salt,  how  much  zinc  would  be  deposited  in  the  same  time? 

4.  How  could  a  silver  cup  be  given  a  gold  lining  by  use  of  the 
electric  current? 

5.  If  the  terminals  of  a  battery  are  immersed  in  a  glass  of  acidulated 
water,  how  can  you  tell  from  the  rate  of  evolution  of  the  gases  at  the 
two  electrodes  which  is  positive  and  which  is  negative  ? 

6.  The  coulomb  (§  305)  is  3  billion  times  as  large  as  the  electrostatic 
unit  of  quantity  denned  in  §  280.    How  many  electrons  pass  per  second 
by  a  given  point  on  a  lamp  filament  which  is  carrying  1  ampere  of 
current  (see  §  284)  ? 


252 


ELECTRICITY  IN  MOTION 


MAGNETIC  EFFECTS  OF  THE  CURRENT  ;  PROPERTIES 
OF  COILS 

306.  Shape  of  the  magnetic  field  about  a  current.  If  we  place 
the  wire  which  connects  the  plates  of  a  galvanic  cell  in  a  vertical  posi- 
tion (Fig.  249)  and  explore  with  a  compass  needle  the  shape  of  the 
magnetic  field  about  the  current,  we  find  that  the  magnetic  lines  are 
concentric  circles  lying  in  a  plane  perpendicular  to  the  wire  and  having 


FIG.  249  FIG. 250 

Magnetic  field  about  a  current 

the  wire  as  their  common  center.  We  find,  moreover,  that  reversing  the 
current  reverses  the  direction  of  the  needle.  If  the  current  is  very  strong 
(say  40  amperes),  this  shape  of  the  field  can  be  shown  by  scattering  iron 
filings  on  a  plate  through  which  the  current  passes  (Fig.  249).  If  the  cur- 
rent is  weak,  the  experiment  should  be  performed  as  indicated  in  Fig.  250. 

The  relation  between  the 
direction  in  which  the  current 
flows  and  the  direction  in  which 
the  N  pole  of  the  needle  points 
(this  is,  by  definition,  the  direc- 
tion of  the  magnetic  field)  is  given  in  the  following  conven- 
ient rule,  known  as  Ampere's  Rule :  If  the  right  hand  grasps 
the  wire  as  in  Fig.  251,  so  that  the  thumb  points  in  the  direction 
in  which  the  current  is  flowing,  then  the  magnetic  lines  encircle 
the  wire  in  the  same  direction  as  do  the  fingers  of  the  hand. 


FIG.  251.   The  right-hand  rule 


MAGNETIC  EFFECTS  OF  THE  CURRENT        253 


\\ 


307.  Loop  of  wire  carrying  a  current  equivalent  to  a  magnet 
disk.     Let  a  single  loop  of  wire  be  suspended  from  a  thread'in  the 
manner  shown  in  Fig.  252,  so  that  its  ends  dip  into  two  mercury  cups. 
Then  let  the  current  from  three  or  four  dry  cells 
be  sent  through  the  loop.   The  latter  will  be  found 
to  slowly  set  itself  so  that  the  face  of  the  loop  from 
which  the  magnetic  lines  emerge,  as  given  by  the 
right-hand  rule  (see  §  306  and  also  Fig.  253),  is 
toward  the  north.    Let  a  bar  magnet  be  brought 
near  the  loop.    The  latter  will  be  found  to  behave 
toward    the  magnet   in  all  respects  as  though  it 

were  a  flat  magnetic 

disk  whose  boundary 

is   the  wire,  the  face 

which     turns    toward 

the  north  being  an  N 

pole  and  the  other  an 

S  pole. 


FIG.  252.    A  loop 

equivalent  to  a  flat 

magnetic  disk 


FIG.  253.  North  pole  of  disk 
is  face  from  which  magnetic 
lines  emerge ;  south  pole  is 
face  into  which  they  enter 


The  experiment  shows  what  posi- 
tion a  loop  bearing  a  current  will 
always  tend  to  assume  in  a  magnetic 
field ;  for,  since  a 
magnet  will  always 
tend  to  set  itself 

so  that  the  line  connecting  its  poles  is  par- 
allel to  the  direction  of  the  magnetic  lines 
of  the  field  in  which  it  is  placed,  a  loop 
must  set  itself  so  that  a  line  connecting  its 
magnetic  poles  is  parallel  to  the  lines  of  the 
magnetic  field,  that  is,  so  that  the  plane  of 
the  loop  is  perpendicular  to  the  field  (see 
Fig.  254);  or,  to  state  the  same  thing  in 
slightly  different  form,  if  a  loop  of  wire, 
free  to  turn,  is  carrying  a  current  in  a  mag- 
netic field,  the  loop  will  set  itself  so  as  to  include  as  many  as 
possible  of  the  lines  of  force  of  the  field. 


FIG.  254.  Position 
assumed  by  a  loop 
carrying  a  current 
in  a  magnetic  field 


254 


ELECTRICITY  IN  MOTION 


308.  Helix  carrying  a  current  equivalent  to  a  bar  magnet. 

Let  a  wire  bearing  a  current  be  wound  in  the  form  of  a  helix  and  held 
near  a  suspended  magnet,  as  in  Fig.  255.  It  will  be  found  to  act  in 
every  respect  like  a  magnet,  with  an  TV 
pole  at  one  end  and  an  £  pole  at  the  other. 


FIG.  255.    Magnetic  effect 
of  a  helix 


This  result  might  have  been  pre- 
dicted from  the  fact  that  a  single 
loop  is  equivalent  to  a  flat-disk 
magnet ;  for  when  a  series  of  such 
disks  is  placed  side  by  side,  as  in  the 
helix,  the  result  must  be  the  same  as  placing  a  series  of  disk 
magnets  in  a  row,  the  N  pole  of  one  being  directly  in  contact 
with  the  S  pole  of  the  next,  etc.  These  poles  would  therefore 
all  neutralize  each  other  except 
at  the  two  ends.  We  therefore 
get  a  magnetic  field  of  the  shape 
shown  in  Fig.  256,  the  direction  of 
the  arrows  representing  as  usual 
the  direction  in  which  an  N  pole 
tends  to  move. 

The  right-hand  rule  as  given 
in  §  306  is  sufficient  in  every  case  to  determine  which  is  the  JV 
and  which  the  S  pole  of  a  helix,  that  is,  from  which  end  the 
lines  of  magnetic  force  emerge  from  the  helix  and  at  which 
end  they  enter  it.  But  it  is  found  con- 
venient, in  the  consideration  of  coils, 
to  restate  the  right-hand  rule  in  a 
slightly  different  way,  thus :  If  the  coil 
is  grasped  in  the  right  hand  in  such  a 
way  that  the  fingers  point  in  the  direc- 
tion in  which  the  current  is  flowing  in 
the  wires,  the  thumb  will  point  in  the  direction  of  the  north  pole 
of  the  helix  (see  Fig.  257).  Similarly,  if  the  sign  of  the  poles 
is  known,  but  the  direction  of  the  current  unknown,  it  may 


FIG.  256.  Magnetic  field  of  helix 


FIG.  257.   Rule  for  poles 
of  helix 


MAGNETIC  EFFECTS  OF  THE  CURRENT        255 


be  determined  as  follows :  If  the  right  hand  is  placed  against 
the  coil  with  the  thumb  pointing  in  the  direction  of  the  lines  of 
force  (that  is,  toward  the  north  pole 
of  the  helix),  the  fingers  will  pass 
around  the  coil  in  the  direction  in 
which  the  current  is  flowing. 


FIG.  258.   The  bar  electro- 
magnet 


309.  The   electromagnet.     Let  a 

core  of  soft  iron  be  inserted  in  the  helix 
(Fig.  258).  The  poles  will  be  found  to  be 
enormously  stronger  than  before.  This 
is  because  the  core  is  magnetized  by  induction  from  the  field  of  the 
helix  in  precisely  the  same  way  in  which  it  w7ould  be  magnetized  by 
induction  if  placed  in  the  field  of  a  perma- 
nent magnet.  The  new  field  strength  about 
*the  coil  is  now  the  sum  of  the  fields  due 
to  the  core  and  that  due  to  the  coil.  If  the 
current  is  broken,  the  core  will  at  once 
lose  the  greater  part  of  its  magnetism.  If 
the  current  is  reversed,  the  polarity  of  the 
core  will  be  reversed.  Such  a  coil  with  a 
soft-iron  core  is  called  an  electromagnet. 


FIG.  259.   The  horseshoe 
electromagnet 


The  strength  of  an  electromagnet 
can  be  very  greatly  increased  by  giving  it  such  form  that 
the  magnetic  lines  can  remain  in  iron  throughout  their  entire 
length  instead  of  emerging  into  air,  as  they 
do  in  Fig.  258.  For  this  reason  electro- 
magnets are  usually  built  in  the  horseshoe 
form  and  provided  with  an  armature  A 
(Fig.  259),  through  which  a  complete  iron 
path  for  the  lines  of  force  is  established,  as 


shown  in  Fig.  260.    The  strength  of  such  a     FIG.  260.  Themag- 
,    T  T       n  .    n  ,1  i          £     netic  circuit  of  an 

magnet  depends  chiefly  upon  the  number  of        electromagnet 

ampere  turns  which  encircle  it,  the  expres- 
sion "  ampere  turns  "  denoting  the  product  of  the  number  of 
turns  of  wire  about  the  magnet  by  the  number  of  amperes 


256  ELECTRICITY  IN  MOTION 

flowing  in  each  turn.  Thus,  a  current  of  -^  ampere  flowing 
1000  times  around  a  core  will  make  an  electromagnet  of 
precisely  the  same  strength  as  a  current  of  1  ampere  flowing 
10  times  about  the  core.  (See  modern  lifting  magnet  opposite 
p.  247.) 

QUESTIONS  AND  PROBLEMS 

1.  Describe  the  magnetic  condition  of  the  space  about  a  trolley  wire 
carrying  a  direct  current. 

2.  In  what  direction  will  the  north  pole  of  a  magnetic  needle  be 
deflected  if  it  is  held  above  a  current  flowing  from  north  to  south  ? 

3.  A  man  stands  beneath  a  north-and-south  trolley  line  and  finds 
that  a  magnetic  needle  in  his  hand  has  its  north  pole  deflected  toward 
the  east.    What  is  the  direction  of  the  current  flowing  in  the  wire? 

4.  A  loop  of  wire  lying  on  the  table  carries  a  current  which  flows 
around  it  in  a  clockwise  direction.    Would  a  north  magnetic  pole  at  the 
center  of  the  loop  tend  to  move  up  or  down? 

5.  If  one  looks  down  on  the  ends  of  a  U-shaped  electromagnet,  does 
the  current  encircle  the  two  coils  in  the  same  or  in  opposite  directions  ? 
Does  it  run  clockwise  or  counterclockwise  about  the  N  pole  ? 

MEASUREMENT  OF  ELECTRIC  CURRENTS 

310.  The  galvanometer.  Electric  currents  are,  in  general, 
measured  by  the  strength  of  the  magnetic  effect  which  they 
are  able  to  produce 
under  specific  condi- 
tions. Thus,  if  the  wire 
carrying  a  current  is 
wound  into  circular 
form,  as  in  Fig.  261,  the 
right-hand  rule  shows 

us   that  the   shape   of 

,,  n   i  !  FIG.  261.   Magnetic  field  about  a  circular  coil 

the   magnetic  field    at  °arrying  a  current 

the  center  of  the  coil 

is  similar  to  that  shown  in  the  figure.    If,  then,  the  coil  is 

placed  in  a  north-and-south  plane  and  a  compass  needle  is 


ANDRE  MARIE  AMPERE  (1775-1836) 

French  physicist  and  mathematician;  son  of  one  of  the  victims 
of  the  guillotine  in  1793 ;  professor  at  the  Polytechnic  School  in 
Paris 'and  later  at  the  College  of  France;  hegan  his  experiments 
on  electromagnetism  in  1820,  very  soon  after  Oersted's  discovery ; 
published  his  great  memoir  on  the  magnetic  effects  of  currents 
in  1823 ;  first  stated  the  rule  for  the  relation  between  the  direction 
of  a  current  in  a  wire  and  the  direction  of  the  magnetic  field 
about  it.  The  ampere,  the  practical  unit  of  current,  is  named 
in  his  honor 


HUGE  ROTOR 

The  figure  shows,  in  process  of  construction,  one  of  the  most  recent  types  of  huge 
generator  of  electricity,  which  are  the  outgrowth  of  the  discovery  of  the  relation 
between  magnetism  and  electricity  to  which  Ampere  contributed  so  much.  The 
figure  shows  in  place  one  of  the  rotating  electromagnets,  which,  as  they  swing 
past  the  huge  coils  of  the  stator  surrounding  them,  at  a  peripheral  speed  of  a  mile 
and  a  half  a  minute,  generate  a  current  of  2700  amperes  at  12,000  volts.  This  is 
one  of  the  three  32,500-kilowatt  machines  built  for  installation  at  Niagara  Falls 


MEASUREMENT  OF  ELECTRIC  CURRENTS      257 


262.      Simple 
suspended-coil  gal- 
vanometer 


placed  at  the  center,  the  passage  of  the  current  through  the 
coil  tends  to  deflect  the  needle  so  as  to  make  it  point  east 
and  west.  The  amount  of  deflection  under  these  conditions 
is  taken  as  the  measure  of  current  strength. 
The  unit  of  current,  the  ampere,  is  in  fact 
approximately  the  same  as  the  current  which, 
flowing  through  a  circular  coil  of  three 
turns  and  10  centimeters  radius,  set  in  a 
north-and-south  plane,  will  produce  a  deflec- 
tion of  45  degrees  at  Washington  in  a  small 
compass  needle  placed  at  its  center.  The 
legal  definition  of  the  ampere  is,  however, 
based  on  the  chemical  effect  of  a  current. 
It  was  given  in  §  305. 

Nearly  all  current-measuring  instruments  consist  essentially 
either  of  a  small  compass  needle  at  the  center  of  a  fixed  coil,  as 
in  Fig.  261,  or  of  a  movable  coil  sus- 
pended between  the  poles  of  a  fixed 
magnet  in  the  manner  illustrated 
roughly  in  Fig.  262.  The  passage 
of  the  current  through  the  coil  pro- 
duces a  deflection,  in  the  first  case, 
of  the  magnetic  needle  with  ref- 
erence to  the  fixed  coil,  and,  in  the 
second  case,  of  the  coil  with  refer- 
ence to  the  fixed  magnet.  If  the 
instrument  has  been  calibrated  to 
give  the  strength  of  the  current 
directly  in  amperes,  it  is  called  an 
ammeter:,  otherwise,  a  galvanometer 
(Fig.  263). 

311.  The  commercial  ammeter.  Fig.  264  shows  the  con- 
struction of  the  usual  form  of  commercial  ammeter.  The 
coil  c  is  pivoted  on  jewel  bearings  and  is  held  at  its  zero 


FIG.  263.    A  lecture-table 
galvanometer 


258 


ELECTRICITY  IN  MOTION 


position  by  a  spiral  spring  p.  When  a  current  flows  through 
the  instrument,  if  it  were  not  for  the  spring  p  the  coil  would 
turn  through  about  120°,  or 
until  its  N  pole  came  oppo- 
site the  S  pole  of  the  magnet 
(see  Fig.  264).  This  zero 
position  of  the  coil  is  chosen 
because  it  enables  the  scale 
divisions  to  be  nearly  equal. 
The  conductor  z,  called  a 
shunt,  carries  nearly  all  the 
current  that  enters  the  in- 
strument at  B,  only  an  exceed- 
ingly small  portion  of  it  going 
through  the  moving  coil  c. 
The  shunt  is  usually  placed 
inside  the  instrument  unless 
interchangeable  shunts  are 
desired. 


FIG.  264.    Construction  of  a 
commercial  ammeter 


QUESTIONS  AND  PROBLEMS 

1.  What  is  the  principle  involved  in  the  chemical  method  of  measur- 
ing the  strength  of  an  electric  current  ?  in  the  magnetic  method  ? 

2.  How  could  you  test  whether  or  not  the  strength  of  an  electric 
current  is  the  same  in  all  parts  of  a  circuit?  Try  it. 

3.  Explain  from  the  diagram  of  the  commercial  ammeter  the  principle 
of  the  suspended-coil,  or  d'Arsonval,  type  of  galvanometer. 

4.  In  calibrating  an  ammeter  the  current  which  produces  a  certain 
deflection  is  found  to  deposit  J  g.  of  silver  in  50  min.  What  is  the 
strength  of  the  current? 

5.  When  a  compass  needle  is  placed,  as  in  Fig.  261,  at  the  middle  of 
a  coil  of  wire  which  lies  in  a  north-and-south  plane,  the  deflection  pro- 
duced in  the  needle  by  a  current  sent  through  the  coil  is  approximately 
proportional  to  the  strength  of  the  current,  provided  the  deflection  is 
small,  —  not  more,  for  example,  than  20°  or  25° ;  but  when  the  deflection 
becomes  large, —  say  60°  or  70°, —  it  increases  very  much  more  slowly 
than  does  the  current  which  produces  it.    Can  you  see  any  reason  why 
this  should  be  so  ? 


ELECTEIC  BELL  AND  TELEGRAPH 


259 


ELECTRIC  BELL  AND  TELEGRAPH 

312  The  electric  bell.  The  electric  bell  (Fig.  265)  is  one  of  the 
simplest  applications  of  the  electromagnet.  When  the  button  P  is 
pressed  (Figs.  265  and  266),  the  electric  circuit  of  the  battery  is  closed, 

and  a  current  flows  in  at  A,  through  the 
coils  of  the  magnet,  over  the  closed 
contact  c,  and  out  again  at  B.  But 
as  soon  as  this  current  is  established, 
the  electromagnet  E  pulls  over  the 
armature  «,  and  in  so  doing  breaks 
the  contact  at  c.  This  stops  the  cur- 
rent and  demagnetizes  the  magnet  E. 
The  armature  is  then  thrown  back 
against  c  by  the  elasticity  of  the 
spring  s  which  supports  it.  No  sooner 
is  the  contact  made  at  c  than  the  cur- 
rent again  begins  to  flow  and  the 
former  operation  is  repeated.  Thus 
the  circuit  is  automatically  made  and 
broken  at  c,  and  the  hammer  H  is 
in  consequence  set  into  rapid  vibration 
against  the  rim  of  the  bell. 

313.    The  telegraph.     The    electric 
telegraph    is    another    simple    appli- 


FIG.  265.,,  The  electric  bell 


cation  of  the 
principle  is  illus- 
trated in  Fig. 
267.  As  soon 
as  the  key  K, 

at  Chicago  for  example,  is  closed,  the  current 
flows  over  the  line  to,  we  will  say,  New  York. 
There  it  passes  through  the  electromagnet  m, 
and  thence  back  to  Chicago  through  the  earth. 
•The  armature  b  is  held  down  by  the  electro- 
magnet m  as  long  as  the  key  K  is  kept  closed. 
As  soon  as  the  circuit  is  broken  at  K  the  arma- 
ture is  pulled  up  by  the  spring  d.  By  means  of 
a  clockwork  device  the  tape  c  is  drawn  along  at 
a  un-if  orm  rate  beneath  the  pencil  or  pen  carried 


electromagnet. 


The 


FIG.  266.  Cross  section 
of  electric  push  button 


260 


ELECTRICITY  IN  MOTION 


by  the  armature  b.  A  very  short  time  of  closing  of  K  produces  a  dot  upon 
the  tape  ;  a  longer  time,  a  dash.  As  the  Morse,  or  telegraphic,  alphabet 
consists  of  certain  combinations  of  dots  and  dashes,  any  desired  mes- 
sage may  be  sent  from  Chicago  and  recorded  in  New  York.  In  modern 


Chicago 


FIG.  267.    Principle  of  the  telegraph 


practice  the  message  is  not  ordinarily  recorded  on  a  tape,  for  operators 
have  learned  to  read  messages  by  ear,  a  very  short  interval  between  two 
clicks  being  interpreted  as  a  dot,  a  longer  interval  as  a  dash. 

The  first  commercial  telegraph  line  was  built  by  S.  F.  B.  Morse  (see 
on  opposite  page)  between  Baltimore  and  Washington.  It  was  opened 
on  May  24,  1844,  with  the  now  famous  message,  "What  hath  God 
wrought ! " 

314.  The  relay  and  sounder.    Since  the  current  that  comes  over  a 
long  telegraph  line  is  of  small  amperage,  the  armature  of  the  electro- 
magnet of  the  receiving  instrument  must  be  made  very  light  to  respond 
to  the  action  of  the  cur- 
rent.   The  electromagnet  Armaturet 
of  this  instrument  is  made 
of   many  thousand  turns 
of  fine  wire,  to  secure  the 
requisite  number  of  am- 
pere turns  (§  309)  to  work 
the  armature.    The  clicks 
of  such  an  armature  are 
not  sufficiently  loud  to  be 
read  easily  by  an  operator. 
Hence    at    each    station 

there  is  introduced  a  local  circuit,  which  contains  a  local  battery  and  a 
second  and  heavier  electromagnet,  which  is  called  a  sounder.  The  elec- 
tromagnet on  the  main  line  is  then  called  the  relay  (see  Fig.  268  and 
the  drawings  opposite  p.  261).  The  sounder  has  a  very  heavy  armature 


„  Etectrotnagnef 


Points 

Spring 
Adjusting  Screw 


FIG.  268.   The  relay 


SAMUEL  F.  B.  MORSE  (1791-1872) 

The  inventor  of  the  electromagnetic  recording  telegraph  and  of  the 
dot-and-dash  alphabet  known  by  his  name,  was  born  at  Charles- 
town,  Massachusetts,  graduated  at  Yale  College  in  1810,  invented 
the  commercial  telegraph  in  1832,  and  struggled  for  twelve  years 
in  great  poverty  to  perfect  it  and  secure  its  proper  presentation 
to  the  public.  The  first  public  exhibition  of  the  completed  instru- 
ment was  made  in  1837  at  New  York  University,  signals  being 
sent  through  1700  feet  of  copper  wire.  It  was  with  the  aid  of  a 
$30,000  grant  from  Congress  that  the  first  commercial  line  was 
constructed  in  1844  between  Washington  and  Baltimore 


wt 


ELECTKIC  BELL  AND  TELEGRAPH  261 

(Fig.  269,  A),  which  is  so  arranged  that  it  clicks  both  when  it  is  drawn 

down  by  its  electromagnet  against  the  stop  S  and  when  it  is  pushed 

up  again  by  its  spring,  on  breaking  the  current,  against  the  stop  L 

The    interval   which    elapses    between   these 

two  clicks  indicates  to  the  operator  whether  a 

dot  or  a  dash  is  sent.    The  small  current  in  the 

main  line  simply  serves  to  close  and  open  the 

circuit   in  the  local  battery  which  operates 

the  sounder  (see  drawings  on  opposite  page). 

The    electromagnets    of    the    relay   and    the 

sounder  differ  in  that  the  latter  consists  of  a 

few  hundred  turns  of  coarse  wire  and  carries     FlG>  269'    The  sounder 

a  comparatively  large  current. 

315.  Plan  of  a  telegraphic  system.  The  actual  arrangement  of  the 
various  parts  of  a  telegraphic  system  is  shown  in  the  drawings  on  the 
opposite  page.  When  an  operator  at  Chicago  wishes  to  send  a  message 
to  New  York,  he  first  opens  the  switch  which  is  connected  to  his  key, 
and  which  is  always  kept  closed  except  when  he  is  sending  a  message. 
He  then  begins  to  operate  his  key,  thus  controlling  the  clicks  of  both 
his  own  sounder  and  that  at  New  York.  When  the  Chicago  switch  is 
closed  and  the  one  at  New  York  open,  the  New  York  operator  is  able  to 
send  a  message  back  over  the  same  line.  In  practice  a  message  is  not 
usually  sent  as  far  as  from  Chicago  to  New  York  over  a  single  line, 
save  in  the  case  of  transoceanic  cables.  Instead  it  is  automatically 
transferred,  say  at  Cleveland,  to  a  second  line,  which  carries  it  on  to 
Buffalo,  where  it  is  again  transferred  to  a  third  line,  which  carries 
it  on  to  New  York.  The  transfer  is  made  in  precisely  the  same  way 
as  the  transfer  from  the  main  circuit  to  the  sounder  circuit.  If,  for 
example,  the  sounder  circuit  at  Cleveland  is  lengthened  so  as  to  extend 
to  Buffalo,. and  if  the  sounder  itself  is  replaced  by  a  relay  (called  in 
this  case  a  repeater),  and  the  local  battery  by  a  line  battery,  then  the 
sounder  circuit  has  been  transformed  into  a  repeater  circuit,  and  all  the 
conditions  are  met  for  an  automatic  transfer  of  the  message  at  Cleveland. 

QUESTIONS  AND  PROBLEMS 

1.  Draw  a  diagram  showing  how  an  electric  bell  works. 

2.  Draw  a  diagram  of  a  short  two-station  telegraph  line  which  has 
only  one  instrument  at  each  station. 

3.  Draw  a  diagram  showing  how  the  relay  and  sounder  operate  in  a 
telegraphic  circuit.    Why  is  a  relay  used? 


262      .  ELECTRICITY  IN  MOTION 

RESISTANCE  AND  ELECTROMOTIVE  FORCE 

316.  Electrical  resistance.*  Let  the  circuit  of  a  galvanic  cell  be 
connected  through  a  lecture-table  ammeter,  or  any  low-resistance  gal- 
vanometer, and,  for  example,  20  feet  of  No.  30  copper  wire,  and  let  the 
deflection  of  the  needle  be  noted.  Then  let  the  copper  wire  be  replaced 
by  an  equal  length  of  No.  30  German-silver  wire.  The  deflection  will 
be  found  to  be  a  very  small  fraction  of  what  it  was  at  first. 

A  cell,  therefore,  which  is  capable  of  developing  a  certain 
fixed  electrical  pressure  is  able  to  force  very  much  more 
current  through  a  given  wire  of  copper  than  through  an 
exactly  similar  wire  of  German  silver.  We  say,  therefore, 
that  German  silver  offers  a  higher  resistance  to  the  passage 
of  electricity  than  does  copper.  Similarly,  every  particular 
substance  has  its  own  characteristic  power  of  transmitting 
electrical  currents.  Since  silver  is  the  best  conductor  known, 
resistances  of  different  substances  are  commonly  referred  to 
it  as  a  standard,  and  the  ratio  between  the  resistance  of  a. 
given  wire  of  any  substance  and  the  resistance  of  an  exactly 
similar  silver  wire  is  called  the  specific  resistance  of  that  sub- 
stance. The  specific  resistances  of  some  of  the  commoner 
metals  in  terms  of  silver  are  given  below: 

Silver  .  .  .  1.00  Soft  iron  .  .  G.OO  German  silver  18.1 
Copper  .  .  .  1.11  Platinum  .  .  7.20  Mercury.  .  .  63.1 
Aluminium.  .  1.87  Hard  steel  .  .  13.5  Nichrome  .  .  66.6 

The  resistance  of  any  conductor  is  directly  proportional  to 
its  length  and  inversely  proportional  to  the  area  of  its  cross 
section  or  to  the  square  of  its  diameter. 

The  unit  of  resistance  is  the  ohm,  named  after  Georg  Ohm 
(see  opposite  p.  268).  A  length  of  9.35  feet  of  No.  30  copper 

*  This  subject  should  be  accompanied  and  followed  by  laboratory  experi- 
ments on  Ohm's  law,  on  the  comparison  of  wire  resistances,  and  on  the 
measurement  of  internal  resistances.  See,  for  example,  Experiments  32,  33, 
and  34  of  the  authors'  Manual. 


RESISTANCE  AND  ELECTROMOTIVE  FORCE    263 

wire,  or  6.2  inches  of  No.  30  German-silver  wire,  has  a 
resistance  of  about  one  ohm.  The  legal  definition  of  the  ohm 
is  a  resistance  equal  to  that  of  a  column  of  mercury  106.3 
centimeters  long  and  1  square  millimeter  in  cross  section,  at  0°  0. 

317.  Resistance  and  temperature.    Let  the  circuit  of  a  galvanic 
cell  be  closed  through  a  galvanometer  of  very  low  resistance  and  about 
10  feet  of  No.  30  iron  wire  wrapped  about  a  strip  of  asbestos.    Let  the 
deflection  of  the  galvanometer  be  observed  as  the  wire  is  heated  in  a 
Bunsen  flame.   As  the  temperature  rises  higher  and  higher  the  current 
will  be  found  to  fall  continually. 

The  experiment  shows  that  the  resistance  of  iron  increases 
with  rising  temperature.  This  is  a  general  law  which  holds  for 
all  metals.  In  the  case  of  liquid  conductors,  on  the  other  hand, 
the  resistance  usually  decreases  with  increasing  temperature. 
Carbon  and  a  few  other  solids  show  a  similar  behavior,  the 
filament  in  the  early  form  of  incandescent  electric  lamp 
having  only  about  half  the  resistance  when  hot  which  it  has 
when  cold. 

318.  Electromotive  force  and  its  measurement.*    The  poten- 
tial difference  which  a  galvanic  cell  or  any  other  generator  of 
electricity  is  able  to  maintain  between  its  terminals  when 
these  terminals  are  not  connected  by  a  wire  —  that  is,  the  total 
electrical  pressure  which  the  generator  is  capable  of  exerting  — 
is  commonly  called  its  electromotive  force,  usually  abbreviated 
to  E.M.F.     TJie  E.M.F.  of  an  electrical  generator  may  be  de- 
fined as  its  capacity  for  producing  electrical  pressure,  or  P.D. 
This  P.D.  might  be  measured,  as  in  §  294,  by  the  deflection 
produced  in  an  electroscope  when  one  terminal  is  connected 
to  the  case  of  the  electroscope  and  the  other  terminal  to  the 
knob.    Potential  differences  are,  in  fact,  measured  in  this  way 
in  all  so-called  electrostatic  voltmeters. 

*  This  subject  should  be  preceded  or  accompanied  by  laboratory  work  on 
E.M.F.  See,  for  example,  Experiment  31  of  the  authors'  Manual. 


264 


ELECTKICITY  IN  MOTION 


#1- 


FIG.  270.    Hydrostatic 

analogy  of  the  action 

of  a  galvanic  cell 


The  more  common  type  of  potential-difference  measurer 
consists,  however,  of  an  instrument  made  like  a  galvanometer 
(Fig.  268),  except  that  the  coil  of  wire  is  made  of  very  many 
turns  of  extremely  fine  wire,  so  that  it 
carries  a  very  small  current.  The  amount 
of  current  which  it  does  carry,  however, 
is  proportional  to  the  difference  in  elec- 
trical pressure  existing  between  its  ends 
when  these  are  touched  to  the  two  points 
whose  P.D.  is  sought.  The  principle  un- 
derlying this  type  of  voltmeter  will  be 
better  understood  from  a  consideration 
of  the  following  water  analogy.  If  the 
stopcock  K  (Fig.  270)  in  the  pipe  con- 
necting the  water  tanks  C  and  D  is  closed, 
and  if  the  water  wheel  A  is  set  in  motion 
by  applying  a  weight  IF,  the  wheel  will  turn  until  it  creates 
such  a  difference  in  the  water  levels  between  C  and  D  that 
the  back  pressure  against  the  left  face  of  the  wheel  stops  it 
and  brings  the  weight  Wto  rest.  In  precisely 
the  same  way  the  chemical  action  within  the 
galvanic  cell  whose  terminals  are  not  joined 
(Fig.  271)  develops  positive  and  negative 
charges  upon  these  terminals ;  that  is,  creates 
a  P.D.  between  them  until  the  back  electrical 
pressure  through  the  cell  due  to  this  P.D.  is 
sufficient  to  put  a  stop  to  further  chemical 
action.  The  seat  of  the  E.M.F.  is  at  the  sur- 
faces of  contact  of  the  metals  with  the  acid, 
where  the  chemical  actions  take  place. 

Now,  if  the  water  reservoirs  (Fig.  270)  are 
put  in  communication  by  opening  the  stopcock  K,  the  differ- 
ence in  level  between  C  and  D  will  begin  to  fall,  and  the 
wheel  will  begin  to  build  it  up  again.  But  if  the  carrying 


FIG.  271.  Meas- 
urement of  P.D. 
between  the  ter- 
minals of  a  gal- 
vanic cell 


RESISTANCE  AND  ELECTROMOTIVE  FORCE    265 

capacity  of  the  pipe  ab  is  small  in  comparison  with  the  capac- 
ity of  the  wheel  to  remove  water  from  D  and  supply  it  to  (7, 
then  the  difference  of  level  which  permanently  exists  between 
C  and  D  when  K  is  open  will  not  be  appreciably  smaller  than 
when  it  is  closed.  In  this  case  the  current  which  flows  through 
ab  may  obviously  be  taken  as  a  measure  of  the  difference 
in  pressure  which  the  pump  is  able  to  maintain  between  C 
and  D  when  K  is  closed. 

In  precisely  the  same  way,  if  the  terminals  C  and  D  of 
the  cell  (Fig.  271)  are  connected  by  attaching  to  them  the 
terminals  a  and  b  of  any  conductor,  they  at  once  begin  to 
discharge  through  this  conductor,  and  their  P.D.  therefore 
begins  to  fall.  But  if  the  chemical  action  in  the  cell  is  able 
to  recharge  C  and  D  very  rapidly  in  comparison  with  the 
ability  of  the  wire  to  discharge  them,  then  the  P.D.  between 
C  and  D  will  not  be  appreciably  lowered 
by  the  presence  of  the  connecting  conductor. 
In  this  case  the  current  which  flows  through 
the  conducting  coil,  and  therefore  the  deflec- 
tion of  the  needle  at  its  center,  may  be 
taken  as  a  measure  of  the  electrical  pres- 
sure developed  by  the  cell,  that  is,  of  the 

P.D.  between  its  unconnected  terminals. 

FIG.  272.    Lecture- 
Ihe    common   voltmeter    (Fig.  272)    is,        table  voltmeter 

then,  exactly  like  an  ammeter,  save  that  it 
offers  so  high  a  resistance  to  the  passage  of  electricity  through 
it  that  it  does  not  appreciably  reduce  the  P.D.  between  the 
points  to  which  it  is  connected. 

319.  The  commercial  voltmeter.  Fig.  273  shows  the  con- 
struction of  the  common  form  of  commercial  voltmeter.  It  dif- 
fers from  the  ammeter  (Fig.  264)  in  that  the  shunt  is  omitted, 
and  a  high-resistance  coil  R  is  put  in  series  with  the  moving 
coil  c.  The  resistance  of  a  voltmeter  may  be  many  thousand 
ohms.  The  current  that  passes  through  it  is  very  small. 


266 


ELECTRICITY  IN  MOTION 


320.  The  electromotive  forces  of  galvanic  cells.  Let  a  voltmeter 
of  any  sort  be  connected  to  the  terminals  of  a  simple  galvanic  cell,  like 
that  of  Fig.  242.  Then  let  the  distance  between  the  plates  and  the 
amount  of  their  immersion  be 
changed  through  wide  limits.  It 
will  be  found  that  the  deflection 
produced  is  altogether  independent 
of  the  shape  or  size .  of  the  plates 
or  their  distance  apart.  But  if  the 
nature  of  the  plates  is  changed, 
the  deflection  changes.  Thus,  while 
copper  and  zinc  in  dilute  sulphuric 
acid  have  an  E.M.F.  of  one  volt, 
carbon  and  zinc  show  an  E.M.F. 
of  at  least  1.5  volts,  while  carbon 
and  copper  will  show  an  E.M.F.  of 
very  much  less  than  a  volt.  Sim- 
ilarly, by  changing  the  nature  of 
the  liquid  in  which  the  plates  are 
immersed,  we  can  produce  changes 
in  the  deflection  of  the  voltmeter.* 


FIG.  273.    Principle  of  commercial 
voltmeter 


We  learn,  therefore,  that  the  E.M.F.  of  a  galvanic  cell  depends 
simply  upon  the  materials  of  which  the  cell  is  composed,  and  not 
at  all  upon  the  shape,  size,  or  distance  apart  of  the  plates. 

321.  Fall  of  potential  along  a  conductor  carrying  a  current. 
Not  only  does  a  P.D.  exist  between  the  terminals  of  a  cell  on 
open  circuit,  but  also  between  any  two  points  on  a  conductor 
through  which  a  current  is  passing.  For  example,  in  the 
electrical  circuit  shown  in  Fig.  274  the  potential  at  the  point 
a  is  higher  than  that  at  m,  that  at  m  higher  than  that  at  n, 
etc.,  just  as,  in  the  water  circuit  shown  in  Fig.  275,  the 


*  A  vertical  lecture-table  voltmeter  (Fig.  272)  and  a  similar  ammeter  are 
desirable  for  this  and  some  of  the  following  experiments,  but  homemade 
high-  and  low-resistance  galvanometers,  like  those  described  in  the  authors' 
Manual,  are  thoroughly  satisfactory,  save  for  the  fact  that  one  student  must 
take  the  readings  for  the  class. 


RESISTANCE  AND  ELECTROMOTIVE  FORCE    26T 


FIG.  274.  Showing  method  of 
connecting  voltmeter  to  find 
P.D.  between  any  two  points 
m  and  n  on  an  electrical  circuit 


hydrostatic  pressure  at  a  is  greater 
than  that  at  m,  that  at  m  greater 
than  that  at  n,  etc.  The  fall  in  the 
water  pressure  between  m  and  n 
(Fig.  275)  is  measured  by  the  water 
head  n's.  If  we  wish  to  measure  the 
fall  in  electrical  potential  between 
m  and  n  (Fig.  274),  we  touch  the 
terminals  of  a  voltmeter  to  these 
points  in  the  manner  shown  in  the 
figure.  Its  reading  gives  us  at  once 
the  P.D.  between  m  and  n  in  volts, 
provided  always  that  its  own  current- 
carrying  capacity  is  so  small  that  it 
does  not  appreciably  lower  the  P.D.  between  the  points  m 
and  n  by  being  touched  across  them ;  that  is,  provided  the 
current  which  flows  through  it  is  neg- 
ligible in  comparison  with  that  which 
flows  through  the  conductor  which 
already  joins  the  points  m  and  n. 

322.  Ohm's  law.  In  1826  Ohm 
announced  the  discovery  that  the 
currents  furnished  ly  different  gal- 
vanic cells,  or  combinations  of  cells, 
are  alivays  directly  proportional  to 
the  E.M.FSs  existing  in  the  circuits  in 
which  the  currents  flow,  and  inversely 
proportional  to  the  total  resistances  of 
these  circuits ;  that  is,  if  /  represents 
the  current  in  amperes,  E  the  E.M.F. 
in  volts,  and  R  the  resistance  of  the 
circuit  in  ohms,  then  Ohm's  law  as  applied  to  the  complete  cir- 


m 


R 


rt 


FIG.  275.    Hydrostatic  anal- 
ogy of  fall  of  potential  in  an 
electrical  circuit 


cuit  is 


TT 

/=  —  ;  that  is,  current  = 


electromotive  force 
resistance 


268  ELECTRICITY  IN  MOTION 

As  applied  to  any  portion  of  an  electrical  circuit,  Ohm's 
law  is 

J=  ££ .  that  is,  current  =  Potential  difference  ^ 
R  resistance 

where  P.D.  represents  the  difference  of  potential  in  volts  be- 
tween any  two  points  in  the  circuit,  and  R  the  resistance  in 
ohms  of  the  conductor  connecting  these  two  points.  This  is 
one  of  the  most  important  laws  in  physics. 

Both  of  the  above  statements  of  Ohm's  law  are  included 

in  the  equation 

volts  ,ON 

amperes  =  — •  (3) 

ohms 

323.  Internal  resistance  of  a  galvanic  cell.  Let  the  zinc  and 
copper  plates  of  a  simple  galvanic  cell  be  connected  to  an  ammeter,  and 
the  distance  between  the  plates  then  increased.  The  deflection  of  the 
needle  will  be  found  to  decrease,  or  if  the  amount  of  immersion  is 
decreased,  the  current  also  will  decrease. 

Now,  since  the  E.M.F.  of  a  cell  was  shown  in  §  320  to  be 
wholly  independent  of  the  area  of  the  plates  immersed  or  of 
the  distance  between  them,  it  will  be  seen  from  Ohm's  law 
that  the  change  in  the  current  in  these  cases  must  be  due  to 
some  change  in  the  total  resistance  of  the  circuit.  Since  the 
wire  which  constitutes  the  outside  portion  of  the  circuit  has 
remained  the  same,  we  must  conclude  that  the  liquid  within 
the  cell,  as  well  as  the  external  wire,  offers  resistance  to  the  pas- 
sage of  the  current.  This  internal  resistance  of  the  liquid  is 
directly  proportional  to  the  distance  between  the  plates,  and 
inversely  proportional  to  the  area  of  the  immersed  portion  of 
the  plates.  If,  then,  we  represent  the  external  resistance  of  the 
circuit  of  a  galvanic  cell  by  Re  and  the  internal  by  R^  Ohm's 
law  as  applied  to  the  entire  circuit  takes  the  form 

(4) 


GEORG  SIMON  OHM  (1787-1854) 

German  physicist  and  discoverer  of  the  famous  law  in  physics 
which  bears  his  name.  He  was  born  and  educated  at  Erlangen. 
It  was  in  1826,  while  he  was  teaching  mathematics  at  a  gym- 
nasium in  Cologne,  that  he  published  his  famous  paper  on  the 
experimental  proof  of  his  law.  At  the  time  of  his  death  he  was 
professor  of  experimental  physics  in  the  university  at  Munich. 
The  ohm,  the  practical  unit  of  resistance,  is  named  in  his  honor 


<c 

ll 


r 


<»  ' 

f  !  i 


-     5  .2  5  ~ 


»r-  G  ~  w  «  a 
§  "a,  S3  *  3  ==  5 
o  g  £  J-  '5  >-.  o 

"*"*     O     gj    "^     ^   "^   5 

bx)  .c  "^  *c      B 

I  a  &1? |1 

•o  t    o  &  5  «*  • 

'o  ^  c  t»  »  .«  ^ 
<»  c  -^  «*  «M 


^  O    O 

PH  £  « 

Q  QJ     •,_! 

^  0^     ° 

§  si 

rt  05  T5 


^  p 


i  .2!  r 


«w     w  ^ 

0    ®    G    S  % 

o>^  2^  e 

«    C  «    »    „,- 


o>  a 

G     U 


S     ««     o   5     «     fi     §" 

g  «g  -C  «  g  .2  1 


sme^i 

<D    bJC •  .S    G    o    O)    e3 

S  "•£    rt    O    §  «w    °° 
a    ca    °  ,C    S    O    en 

O     CJ     1/2  "^ 

| «  ^  i  SJ*| 

II 


RESISTANCE  AND  ELECTROMOTIVE  FORCE    269 

Thus,  if  a  simple  cell  has  an  internal  resistance  of  2  ohms  and  an 
E.M.F.  of  1  volt,  the  current  which  will  flow  through  the  circuit  when 
its  terminals  are  connected  by  9.35  ft.  of  No.  30  copper  wire  (1  ohm)  is 

=  .33  ampere. 

324.  Measurement  of  internal  resistance.    A  simple  and  direct  method 
of  finding  a  length  of  wire  which  has  a  resistance  equivalent  to  the 
internal  resistance  of  a  cell  is  to  connect  the  cell  first  to  an  ammeter 
or  any  galvanometer  of  negligible  resistance*  and  then  to  introduce 
enough  German-silver  wire  into  the  circuit  to  reduce  the  galvanometer 
reading  to  half  its  original  value.  The  internal  resistance  of  the  cell  is 
then  equal  to  that  of  the  German-silver  wire.  Why  ?  A  still  easier  method 
in  case  both  an  ammeter  and  a  voltmeter  are  available  is  to  divide  the 
E.M.F.  of  the  cell  as  given  by  the  voltmeter  by  the  current  which  the  cell 
is  able  to   send  through  the  ammeter  when  connected  directly  to  its 
terminals;   for  in  this  case  Re  of  equation  (4)  is  negligibly  small; 

therefore  R{  =  — .    This  gives  the  internal  resistance  directly  in  ohms. 

325.  Measurement  of  any  resistance  by  ammeter- voltmeter 
method.    The  simplest  way  of  measuring  the  resistance  of  a 
wire,  or,  in  general,  of  any  conductor,  is  to  connect  it  into  the 
circuit  of  a  galvanic  cell  in  the  manner 

shown  in  Fig.  276.  The  ammeter  A  is 
inserted  to  measure  the  current,  and  the 
voltmeter  Fto  measure  the  P. D.  between 
the  ends  a  and  b  of  the  wire  r,  the  resist- 
ance of  which  is  sought.  The  resistance 

of  r  in  ohms  is  obtained  at  once  from  the 

.,  FIG.  276.    Ammeter-volt- 

ammeter  and  voltmeter  readings  with     meter  method  of  meas- 

the  aid  of  the  law  /  =  — ,  from  which  uring  resistance 

JLk/ 

P.D. 

it  follows  that  R  =  — — -  •    Thus,  if  the  voltmeter  indicates  a 

P.D.  of  .4  volt  and  the  ammeter  a  current  of  .5  ampere,  the 
4 

resistance  of  r  is  '--  =  .8  ohm.t 
.o 

*A  lecture-table  ammeter  is  best,  but  see  note  on  page  266. 

t  See  Experiment  33  of  the  authors'  Manual  for  Wheatstone's  bridge  method. 


270 


ELECTRICITY  IX  MOTION 


326.  Joint  resistance  of  conductors  connected  in  series  and  in 
parallel.    When  resistances  are  connected  as  in  Fig.  277,  so 

that  the  same  current  flows 

lOtim     3Ohms        50tims 

o^'YTJr£'Try?rffir>/TBTr^ 


FIG.  277.    Series  connections 


through    each   of   them   in 

succession,  they  are  said  to 

be  connected  in  series.    The 

total  resistance  of  a  number 

of  conductors  so  connected  is  the  sum  of  the  several  resistances. 

Thus,  in  the  case   shown  in  the  figure  the  total  resistance 

between  a  and  b  is  10  ohms. 

When  n  exactly  similar  conductors  are  joined  in  the  manner 
shown  in  Fig.  278,  that  is,  in  parallel  or  multiple,  the  total 
resistance  between  a  and  b  is  \/n  of  the 
resistance  of  one  of  them ;  for  obviously, 
with  a  given  P.D.  between  the  points 
a  and  b,  four  conductors  will  carry  four 
times  as  much  current  as  one,  and  n 
conductors  will  carry  n  times  as  much 
current  as  one.  Therefore  the  resistance, 
which  is  inversely  proportional  to  the 
carrying  capacity  (see  §  322),  is  \/n  as  much  as  that  of  one. 

327.   Shunts.    A  wire  connected  in  parallel  with  another 
wire  is  said  to  be  a  shunt  to  that  wire.    Thus,  the  conductor 
X  (Fig.  279)  is  said  to  be  shunted  across 
the  resistance  R.     Under  such  conditions 
the  currents  carried  by  R  and  X  will  be 
inversely  proportional  to  their  resistances, 
so  that  if  X  is  1  ohm  and  R  is  10  ohms,  R 
will  carry  -^  as  much  current  as  X,  or  -i. 
of   the  whole   current.    In  other  words,  since   the   carrying 
power,  or  conductance,  of  X  is  ten  times  that  of  R,  ten  times 
as  much  current  will  flow  through  X  as  through  R,  or  -j-^-  of 
the  whole  current  will  pass  through  the  shunt.    The  ammeter 
(Fig.  264)  uses  a  shunt  of  exceedingly  small  resistance. 


FIG.  278.  Parallel  con- 
nections 


FIG.  279.    A  shunt 


RESISTANCE  AND  ELECTKOMOTIVE  FORCE    271 


QUESTIONS  AND  PROBLEMS 

1.  How  can  you  prove  that  the  E.M.F.  of  a  cell  does  not  depend 
upon  the  size  or  nearness  of  the  plates  ? 

2.  How  can  you  prove  that  the  internal  resistance  of  a  cell  becomes 
smaller  when  the  plates  are  made  larger  ?  when  placed  closer  together  ? 

3.  If  the  potential  difference  between  the  terminals  of  a  cell  on  open 
circuit  is  to  be  measured  by  means  of  a  galvanometer,  why  must  the 
galvanometer  have  a  high  resistance  ? 

4.  Why  are  iron  wires  used  on  telegraph  lines  but  copper  wires  on 
trolley  systems? 

5.  A  voltmeter  which  has  a  resistance  of  2000  ohms  is  shunted 
across  the  terminals  A  and  B  of  a  wire  which  has  a  resistance  of  1  ohm. 
What  fraction  of  the  total  current  flowing  from  A  to  B  will  be  carried 
by  the  voltmeter  ? 

6.  In  a  given  circuit  the  P.D.  across  the  terminals  of  a  resistance 
of  19  ohms  is  found  to  be  3  volts.   What  is  the  P.D.  across  the  termi- 
nals of  a  3-ohm  wire  in  the  same  circuit  ? 

7.  The  resistance  of  a  certain  piece  of  German-silver  wire  is  1  ohm. 
What  will  be  the  resistance  of  another  piece  of  the  same  length  but  of 
twice  the  diameter  ? 

8.  How  much  current  will  flow  between  two  points  whose  P.D.  is 
2  volts,  if  they  are  connected  by  a  wire  having  a  resistance  of  12  ohms  ? 

9.  What  P.D.  exists  between  the  ends  of  a  wire  whose  resistance  is 
100  ohms  when  the  wire  is  carrying  a  current  of  .3  ampere  ? 

10.  If  a  voltmeter  attached  across  the  terminals  of  an  incandescent 
lamp  shows  a  P.D.  of  110  volts,  while  an  ammeter  connected  in  series 
with  the  lamp  indicates  a  current  of  .5  ampere,  what  is  the  resistance 
of  the  incandescent  filament  ? 

11.  A  certain  storage  cell  having  an  E.M.F.  of  2  volts  is  found  to 
furnish  a  current  of  20  amperes  through  an  ammeter  whose  resistance 
is  .05  ohm.   Find  the  internal  resistance  of  the  cell. 

12.  The  E.M.F.  of  a  certain  battery  is  10  volts  and  the  strength  of 
the  current  obtained  through  an  external  resistance  of  4  ohms  is  1.25 
amperes.    What  is  the  internal  resistance  of  the  battery  ? 

13.  Consider  the  diameter  of  No.  20  wire  to  be  three  times  that  of 
No.  30.   A  certain  No.  30  wire  1  meter  long  has  a  resistance  of  6  ohms. 
What  would  be  the  resistance  of  4  meters  of  No.  20  wire  made  of  the 
same  metal? 

14.  Three  wires,  each  having  a  resistance  of  15  ohms,  were  joined 
in  parallel  and  a  current  of  3  amperes  sent  through  them.    How  much 
was  the  E.M.F.  of  the  current? 


272 


ELECTRICITY  IN  MOTION 


r-*H 


FIG.  280.    Chemical 
actions  in  the  vol- 
taic cell 


PRIMARY  CELLS 

328.  Study  of  the  action  of  a  simple  cell.    If  the  simple  cell 
already  described,  that  is,  zinc  and  copper  strips  in  dilute  sulphuric  acid, 
is  carefully  observed,  it  will  be  seen  that,  so  long  as  the  plates  are  not 
connected  by  a  conductor,  fine  bubbles  of  gas  are 

slowly  formed  at  the  zinc  plate,  but  none  at  the 
copper  plate.  As  soon,  however,  as  the  two  strips 
are  put  into  metallic  connection,  bubbles  appear  in 
great  numbers  about  the  copper  plate  (Fig.  280), 
and  at  the  same  time  a  current  manifests  itself  in 
the  connecting  wire.  These  are  bubbles  of  hydro- 
gen. Their  appearance  on  the  zinc  may  be  pre- 
vented either  by  using  a  plate  of  chemically  pure 
zinc  or  by  amalgamating  impure  zinc,  that  is,  by 
coating  it  over  with  a  thin  film  of  mercury.  But 
the  bubbles  on  the  copper  cannot  be  thus  disposed 
of.  They  are  an  invariable  accompaniment  of  the 

current  in  the  circuit.  If  the  current  is  allowed  to  run  for  a  considerable 
time,  it  will  be  found  that  the  zinc  wastes  away,  even  though  it  has  been 
amalgamated,  but  that  the  copper  plate  does  not  undergo  any  change. 

We  learn,  therefore,  that  the  electrical  current  in  the  simple 
cell  is  accompanied  by  the  eating  up  of  the  zinc  plate  by 
the  liquid,  and  by  the  evolution  of  hydrogen  bubbles  at  the 
copper  plate.  In  every  type  of  galvanic  cell,  actions  similar 
to  these  two  are  always  found ;  that  is,  one  of  the  plates  is 
always  eaten  up,  and  upon  the  other  plate  some  element  is  deposited. 
The  zinc,  which  is  eaten,  is  the  one  which  we  found  to  be 
negatively  charged  when  tested  (§  300),  so  that  when  the 
terminals  are  connected  through  a  wire,  the  negative  electrons 
flow  through  this  wire  from  the  zinc  plate  to  the  copper  plate. 
This  means,  in  accordance  with  the  convention  mentioned  in 
the  footnote  to  §  293,  that  the  direction  of  the  current  thrmtgh 
the  external  circuit  is  always  from  the  uneaten  to  the  eaten  plate. 

329.  Local  action  and  amalgamation.    The  cause  of  the 
appearance  of  the  hydrogen  bubbles   at  the  surface   of  im- 
pure zinc  when  dipped  in  dilute  sulphuric  acid  is  that  little 


PEIMARY  CELLS 


273 


electrical  circuits  are  set  up  between  the  zinc  and  the  small 
impurities  in  it  (carbon  or  iron  particles)  in  the  manner 
indicated  in  Fig.  281.  If  the  zinc  is  pure, 
these  little  local  currents  cannot,  of  course,  be 
set  up,  and  consequently  no  hydrogen  bubbles 
appear.  Amalgamation  stops  this  so-called 
local  action,  because  the  mercury  dissolves  the 
zinc,  while  it  does  not  dissolve  the  carbon, 
iron,  or  other  impurities.  The  zinc-mercury 
amalgam  formed  is  a  homogeneous  substance  which  spreads 
over  the  whole  surface  and  covers  up  the  impurities.  It  is 
important,  therefore,  to  amalgamate  the  zinc  in  a  battery,  in 
order  to  prevent  the  consumption  of  the  zinc  when  the  cell 
is  on  open  circuit.  The  zinc  is  under  all  circumstances  eaten 
up  when  the  current  is  flowing,  amalgamation  serving  only 
to  prevent  its  consumption  when  the  circuit  is  open. 


FIG.  281.  Local 
action 


330.  Theory  of  the  action  of  a  simple  cell.  A  simple  cell  may  be 
made  of  any  two  dissimilar  metals  immersed  in  a  solution  of  any  acid 
or  salt.  For  simplicity  let  us  examine  the  action  of  a  cell  cbmposed  of 
plates  of  zinc  and  copper  immersed  in  a  dilute  solution  of  hydrochloric 
acid.  The  chemical  formula  for  hydrochloric 
acid  is  HC1.  This  means  that  each  molecule 
of  the  acid  consists  of  one  atom  of  hydrogen 
combined  with  one  atom  of  chlorine.  As 
was  explained  under  electrolysis  (§  302),  the 
acid  dissociates  into  positively  and  negatively 
charged  ions  (Fig.  282). 

When  a  zinc  plate  is  placed  in  such  a  solu- 
tion, the  acid  attacks  it  and  pulls  zinc  atoms 
into  solution.  Now,  whenever  a  metal  dis- 
solves in  an  acid,  its  atoms,  for  some  unknown 
reason,  go  into  solution  bearing  little  positive 

charges.  The  corresponding  negative  charges  must  be  left  on  the  zinc  plate 
in  precisely  the  same  way  in  which  a  negative  charge  is  left  on  silk 
when  positive  electrification  is  produced  on  a  glass  rod  by  rubbing  it 
the  silk.  It  is  in  this  way,  then,  that  we  account  for  the  negative 


FIG.  282.  Showing  disso- 
ciation of  hydrochloric- 
acid  molecules  in  water 


274  ELECTRICITY  IN  MOTION 

charge  which  we  found  upon  the  zinc  plate  in  the  experiment  which 
was  performed  with  the  galvanic  cell  and  the  electroscope  (see  §  300). 

The  passage  of  positively  charged  zinc  ions  into  solution  gives  a  posi- 
tive charge  to  the  solution  about  the  zinc  plate,  so  that  the  hydrogen 
ions  tend  to  be  repelled  away  from  this  plate.  When  these  repelled 
hydrogen  ions  reach  the  copper  plate,  some  of  them  give  up  their  charges 
to  it  and  then  collect  as  bubbles  of  hydrogen  gas.  It  is  in  this  way 
that  we  account  for  the  positive  charge  which  we  found  on  the  copper 
plate  in  the  experiment  of  §  300. 

If  the  zinc  and  copper  plates  are  not  connected  by  an  outside  con- 
ductor, this  passage  of  positively  charged  zinc  ions  into  solution  con- 
tinues but  a  very  short  time,  for  the  zinc  soon  becomes  so  strongly  charged 
negatively  that  it  pulls  back  on  the  +  zinc  ions  with  as  much  force  as 
the  acid  is  pulling  them  into  solution.  In  precisely  the  same  way  the 
copper  plate  soon  ceases  to  take  up  any  more  positive  electricity  from 
the  hydrogen  ions,  since  it  soon  acquires  a  large  enough  +  charge  to 
repel  them  from  itself  with  a  force  equal  to  that  with  which  they  are 
being  driven  out  of  solution  by  the  positively  charged  zinc  ions.  It  is 
in  this  way  that  we  account  for  the  fact  that  on  open  circuit  no  chemi- 
cal action  goes  on  in  the  simple  galvanic  cell,  the  zinc  and  copper  plates 
simply  becoming  charged  to  a  definite  difference  of  potential  which  is 
called  the  E.M.F.  of  the  cell. 

When,  however,  the  copper  and  zinc  plates  are  connected  by  a  wire, 
a  current  at  once  flows  from  the  copper  to  the  zinc,  and  the  plates  thus 
begin  to  lose  their  charges.  This  allows  the  acid  to  pull  more  zinc  into 
solution  at  the  zinc  plate,  and  allows  more  hydrogen  to  go  out  of  solution 
at  the  copper  plate.  These  processes,  therefore,  go  on  continuously  so 
long  as  the  plates  are  connected.  Hence  a  continuous  current  flows 
through  the  connecting  wire  until  the  zinc  is  all  eaten  up  or  the 
hydrogen  ions  have  all  been  driven  out  of  the  solution,  that  is,  until 
either  the  plate  or  the  acid  has  become  exhausted. 

331.  Polarization.  If  the  simple  galvanic  cell  described  is  con- 
nected to  a  lecture-table  ammeter  through  two  or  three  feet  of  No.  30 
German-silver  wire,  the  deflection  of  the  needle  will  decrease  slowly ; 
but  if  the  hydrogen  is  removed  from  the  copper  plate  (this  can  be  done 
completely  only  by  removing  and  thoroughly  drying  the  plate),  the 
deflection  will  be  found  to  return  to  its  first  value. 

The  experiment  shows  clearly  that  the  observed  falling  off 
in  current  was  due  to  the  collection  of  hydrogen  about  the 


PKIMAKY  CELLS  275 

copper  plate.    This  phenomenon  of  the  weakening  of  the  cur- 
rent from  a  galvanic  cell  is  called  the  polarization  of  the  celL 

332.  Causes  of  polarization.    The  presence  of  the  hydrogen 
bubbles   on   the  positive  plate   causes   a  diminution  in   the 
strength  of  the  current  for  two  reasons :  first,  since  hydrogen 
is  a  nonconductor,  by  collecting  on  the  plate  it  diminishes  the 
effective  area  of  the  plate  and  therefore  increases  the  internal 
resistance  of  the  cell;  second,  the  collection  of  the  hydrogen 
about  the  copper  plate  lowers  the  E.M.F.  of  the  cell,  because 
it  virtually  substitutes  a  hydrogen  plate  for  the  copper  plate, 
and  we  have  already  seen  (§  320)  that  a  change  in  any  of 
the  materials  of  which  a  cell  is  composed  changes  its  E.M.F. 
That  there  is  a  real  fall  in  E.M.F.  as  well  as  a  rise  in  internal 
resistance  when  a  cell  polarizes  may  be  directly  proved  in 
the  following  way: 

Let  the  deflection  of  a  lecture-table  voltmeter  whose  terminals  are 
attached  to  the  freshly  cleaned  plates  of  a  simple  cell  be  noted.  Then 
let  the  cell's  terminals  be  short-circuited  through  a  coarse  wire  for  half 
a  minute.  As  soon  as  the  wire  is  removed,  the  E.M.F.,  indicated  by  the 
voltmeter,  will  be  found  to  be  much  lower  than  at  first.  It  will,  however, 
gradually  creep  back  toward  its  old  value  as  the  hydrogen  disappears- 
from  the  plate,  but  a  thorough  cleaning  and  drying  of  the  plate  will  be 
necessary  to  restore  completely  the  original  E.M.F. 

The  different  forms  of  galvanic  cells  in  common  use  differ 
chiefly  in  different  devices  employed  either  for  disposing  of 
the  hydrogen  bubbles  or  for  preventing  their  formation. 
The  most  common  types  of  such  cells  are  described  in  the 
following  sections. 

333.  The  Daniell  cell.     The  Daniell  cell  consists  of  a  zinc  plate 
immersed  in  zinc  sulphate  and  a  copper  plate  immersed  in  copper  sul- 
phate, the  two  liquids  being  kept  apart  either  by  means  of  an  unglazed 
earthen  cup,  as  in  the  type  shown  in  Fig.  283,*  or  else  by  gravity. 

*  To  set  up,  fill  the  battery  jar  with  a  saturated  solution  of  copper  sul- 
phate. Fill  the  porous  cup  with  water  and  add  a  handful  of  zinc  sulphate 
crystals. 


276 


ELECTEICITY  IK  MOTION 


FIG.  283.   The  Daniell  cell 


In  this  cell  polarization  is  almost  entirely  avoided,  for  the  reason  that 
no  opportunity  is  given  for  the  formation  of  hydrogen  bubbles;  for, 
just  as  the  hydrochloric  acid  solution  described  in  §  330  consists  of 
positive  hydrogen  ions  and  negative  chlorine  ions  in  water,  so  the  zinc 
sulphate  (ZnSO4)  solution  consists  of  positive  zinc 
ions  and  negative  SO4  ions,  and  the  copper  sulphate 
solution  of  positive  copper  ions 
and  negative  SO4  ions.  Now  the 
zinc  of  the  zinc  plate  goes  into 
solution  in  the  zinc  sulphate  in 
precisely  the  same  way  that  it 
goes  into  solution  in  the  hydro- 
chloric acid  of  the  simple  cell 
described  in  §  330.  This  gives  a 
positive  charge  to  the  solution 
about  the  zinc  plate,  and  causes 
a  movement  of  the  positive  ions 
between  the  two  plates  from  the 

zinc  toward  the  copper,  and  of  negative  ions  in  the  opposite  direction, 
both  the  Zn  and  the  SO4  ions  being  able  to  pass  through  the  porous 
cup.  Since  the  positive  ions  about  the  copper  plate  consist  of  atoms  of 
copper,  it  will  be  seen  that  the  material  which  is  driven  out  of  solution 
at  the  copper  plate,  instead  of  being  hydrogen,  as  in  the  simple  cell,  is 
metallic  copper.  Since,  then,  the  element  which  is  deposited  on  the 
copper  plate  is  the  same  as  that  of  which  it  already  consists,  it  is  clear 
that  neither  the  E.M.F.  nor  the  resistance  of  the  cell  can  be  changed 
because  of  this  deposit;  that  is,  the  cause  of  the  polarization  of  the 
simple  cell  has  been  removed. 

The  great  advantage  of  the  Daniell  cell  lies  in  the  relatively  high 
degree  of  constancy  in  its  E.M.F.  (1.08  volts).  It  has  a  comparatively 
high  internal  resistance  (one  to  six  ohms)  and  is  therefore  incapable  of 
producing  very  large  currents, —  about  one  ampere  at  most.  It  will  fur- 
nish a  very  constant  current,  however,  for  a  great  length  of  time,  in  fact, 
until  all  of  the  copper  is  driven  out  of  the  copper  sulphate  solution.  In 
order  to  keep  a  constant  supply  of  the  copper  ions  in  the  solution,  copper- 
sulphate  crystals  are  kept  in  the  compartment  S  of  the  cell  of  Fig.  283 
or  in  the  bottom  of  the  gravity  cell.  These  dissolve  as  fast  as  the  solution 
loses  its  strength  through  the  deposition  of  copper  on  the  copper  plate. 

The  Daniell  is  a  so-called  "  closed-circuit "  cell ;  that  is,  its  circuit 
should  be  left  closed  (through  a  resistance  of  thirty  or  forty  ohms) 


PRIMARY  CELLS 


277 


FIG.  284.  The  Western 
normal  cell 


whenever  the  cell  is  not  in  use.  If  it  is  left  on  open  circuit,  the  copper 
sulphate  diffuses  through  the  porous  cup,  and  a  brownish  muddy  deposit 
of  copper  or  copper  oxide  is  formed  upon  the  zinc.  Pure  copper  is  also 
deposited  in  the  pores  of  the  porous  cup.  Both  of  these  actions  damage 
the  cell.  When  the  circuit  is  closed,  however,  since  the  electrical  forces 
always  keep  the  copper  ions  moving  toward  the 
copper  plate,  these  damaging  effects  are  to  a 
large  extent  avoided. 

334.  The  Western  normal  cell ;  the  volt. 

This  cell  consists  of  a  positive  electrode 
of  mercury  in  a  paste  of  mercurous  sul- 
phate, and  a  negative  electrode  of  cad- 
mium amalgam  in  a  saturated  solution  of 
cadmium  sulphate  (Fig.  284).  It  is  so 
easily  and  exactly  reproducible  and  has  an 
E.M.F.  of  such  extraordinary  constancy 
that  it  has  been  taken  by  international  agreement  as  the 
standard  in  terms  of  which  all  E.M.F.'s  and  P.D.'s  are  rated. 
Thus  the  E.M.F.  of  a  Weston  normal  cell  at  20°  C.  is  taken  as 
1.0183  volts.  The  legal  definition  of  the  volt  is  then  "  an  electrical 
pressure  equal  to  1  0  *  8  3  of  that  produced  by  a  Weston  normal  celV 

335.  The  Leclanche  cell.     The    Leclanche 
cell  (Fig.  285)  consists  of   a  zinc  rod  in  a 
solution  of  ammonium  chloride  (150  grams  to 
a  liter  of  water)  and  a  carbon  plate  placed 
inside  of  a  porous  cup  which  is  packed  full  of 
manganese  dioxide  and  powdered  graphite  or 
carbon.    As  in  the  simple  cell,  the  zinc  dis- 
solves in  the  liquid,  and  hydrogen  is  liberated 
at  the  carbon,  or  positive,  plate.    Here  it  is 
slowly  attacked  by  the  manganese  dioxide. 

This  chemical  action  is,  however,  not  quick  enough  to  prevent 
rapid  polarization  when  large  currents  are  taken  from  the  cell. 
The  cell  slowly  recovers  when  allowed  to  stand  for  a  while 


FIG.  285.     The 
Leclanche"  cell 


278 


ELECTRICITY  IN  MOTION 


on  open  circuit.  The  E.M.F.  of  a  Leclanche  cell  is  about  1.5 
volts,  and  its  initial  internal  resistance  is  somewhat  less  than 
an  ohm.  It  therefore  furnishes  a  momentary  current  of  from 
one  to  three  amperes. 

The  immense  advantage  of  this  type  of  cell  lies  in  the 
fact  that  the  zinc  is  not  at  all  eaten  by  the  ammonium  chlo- 
ride when  the  circuit  is  open,  and  that  therefore,  unlike  the 
Daniell  cell,  it  can  be  left  for  an  indefinite  time  on  open 
circuit  without  deterioration.  Leclanche  cells  are  used  almost 
exclusively  where  momentary  currents  only  are  needed,  as, 
for  example,  on  doorbell  circuits. 
The  cell  requires  no  attention  for 
years  at  a  time,  other  than  the  oc- 
casional addition  of  water  to  replace 
loss  by  evaporation,  and  the  occa- 
sional addition  of  ammonium  chlo- 
ride (NH4C1)  to  keep  positive  NH4 
and  negative  Cl  ions  in  the  solution. 

336.  The  dry  cell.  The  dry  cell 
(Fig.  286)  is  a  modified  form  of 
Leclanche  cell.  It  is  not  really 
dry,  since  the  mixture  within  is  a 
moist  paste.  The  ordinary  dry  cell 

contains  approximately  100  grams  of  water.  The  zinc  plate 
is  in  the  form  of  a  cylindrical  can  and  holds  the  moist  black 
mixture  in  which  the  carbon  plate  is  embedded.  This  mixture 
consists  of  ammonium  chloride,  black  oxide  of  manganese, 
zinc  chloride,  powdered  petroleum  coke,  and  a  small  amount 
of  graphite.  As  in  the  Leclanche  cell,  it  is  the  action  of  the 
ammonium  chloride  upon  the  zinc  which  produces  the  current. 
The  manganese  dioxide  overcomes  the  polarization  due  to 
hydrogen.  The  function  of  the  ZnCl.2  is  to  overcome  the  polar- 
ization due  to  ammonia.  The  graphite  diminishes  internal 
resistance,  which,  in  a  fresh  cell  of  ordinary  size,  may  be  less 


-  Pitch 
Sand 

•?-$( Carbon  rod 

Moist  Hack 

mixture 

Pulp  board 

lining 

—  Zinc  plate 


FIG.  286.   The  dry  cell 


PEIMAKY  CELLS 


279 


FIG.  287.  Cells  con- 
nected in  series 


than  ^o  of  an  ohm.  Because  of  the  low  internal  resistance 
these  cells  will  deliver  30  or  more  amperes  on  momentary 
short  circuit,  and  on  account  of  their  great  convenience  they  are 
manufactured  by  the  million  annually,  one 
firm  alone  making  as  high  as  30,000  a  day. 
337.  Combinations  of  cells.  There  are  two 
ways  in  which  cells  may  be  combined :  first, 
in  series-,  and,  second,  in  parallel.  When 
they  are  connected  in  series,  the  zinc  of  one 
cell  is  joined  to  the  copper  of  the  second,  the  zinc  of  the  second 
to  the  copper  of  the  third,  etc.,  the  copper  of  the  first  and  the 
zinc  of  the  last  being  joined  to  the  ends  of  the  external  resist- 
ance (see  Fig.  287).  The  E.M.F.  of  such  a  combination  is  the 
sum  of  the  E.M.F.'s  of  the  single  cells. 
The  internal  resistance  of  the  combina- 
tion is  also  the  sum  of  the  internal  resist- 
ances of  the  single  cells.  Hence,  if  the 
external  resistances  are  very  small,  the 
current  furnished  by  the  combination  will 
be  no  larger  than  that  furnished  by  a  single 
cell,  since  the  total  resistance  of  the  circuit 
has  been  increased  in  the  same  ratio  as  the 
total  E.M.F.  But  if  the  external  resist- 
ance is  large,  the  current  produced  by  the 
combination  will  be  very  much  greater 
than  that  produced  by  a  single  cell.  Just 
how  much  greater  can  always  be  deter- 
mined by  applying  Ohm's  law  ;  for  if  there  are  n  cells  in  series, 
and  E  is  the  E.M.F.  of  each  cell,  the  total  E.M.F.  of  the  cir- 
cuit is  nE.  Hence,  if  Re  is  the  external  resistance  and  R{  the 
internal  resistance  of  a  single  cell,  then  Ohm's  law  gives 


ll 

>.    .    .  ^ 

I 

Ri 

3 

0 

b 

e— 

—  . 

]' 

m 

FIG.  288.   Water  anal- 
ogy of  cells  in  series 


T  


nE 


280 


ELECTEICITY  IN  MOTION 


FIG.  289.   Cells 
in  parallel 


FIG.  290.    Water  analogy 
of  cells  in  parallel 


If  the  n  cells  are  connected  in  parallel,  that  is,  if  all  the 
coppers  are  connected  together  and  all  the  zincs,  as  in  Fig.  289, 
the  E.M.F.  of  the  combination  is  only  the  E.M.F.  of  a  single 
cell,  while  the  internal  resistance  is  1/n  of  that  of  a  single 
cell,  since  connecting  the  cells  in  this  way  is  simply  equivalent 
to  multiplying  the  area  of  the  plates  n  times.  The  current 
furnished  by  such  a 
combination  will  be 
given  by  the  formula 


/= 


If,  therefore,  Re  is 
negligibly  small,  as  in 
the  case  of  a  heavy 
copper  wire,  the  current  flowing  through  it  will  be  n  times  as 
great  as  that  which  could  be  made  to  flow  through  it  by  a 
single  cell.  Figs.  288  and  290  show  by  means  of  the  water 
analogy  why  the  E.M.F.  of  cells  in  series  is  the  sum  of  the 
several  E.M.F.'s,  and  why  the  E.M.F.  of  cells  in  parallel  is  no 
greater  than  that  of  a  single  cell.  These  considerations  show 
that  the  rules  which  should  govern  the  combination  of  cells  are 
as  follows :  Connect  in  series  when  Re  is  large  in  comparison  with 
jft . ;  connect  in  parallel  when  R{  is  large  in  comparison  with  Re. 

QUESTIONS  AND  PROBLEMS 

1.  A  certain  dry  cell  having  an  E.  M.  F.   of  1.5  volts  delivered  a 
current  of  30  amperes  through  an  ammeter  having  a  negligible  resist- 
ance.   Find  the  internal  resistance  of  the  cell. 

2.  Why  is  a  Leclanche"  cell  better  than  a  Daniell  cell  for  ringing 
doorbells  ? 

3.  Diagram  three  wires  in  series  and  three  cells  in  series.    If  each 
wire  has  a  resistance  of  .1  ohm,  what  is  the  resistance  of  the  series  ?  If 
each  cell  has  a  resistance  of  .1  ohm,  what  is  the  internal  resistance  of 
the  series? 


SECONDARY  CELLS  281 

4.  Diagram  three  wires  in  parallel  or  multiple,  and  three  cells  in 
multiple.    If  each  wire  has  a  resistance  of  6  ohms,  what  is  the  joint 
resistance  of  the  three  ?   If  each  cell  has  an  internal  resistance  of  6  ohms, 
what  is  the  resistance  of  the  group  ? 

5.  With  the  aid  of  Figs.  288  and  290  discuss  the  water  analogies 
of  the  rules  at  the  end  of  §  337. 

6.  If  the  internal  resistance  of  a  Daniell  cell  of  the  gravity  type  is 
4  ohms,  and  its  E.M.  F.  1.08  volts,  how  much  current  will  40  cells  in 
series  send  through  a  telegraph  line  having  a  resistance  of  500  ohms  ? 
What  current  will  40  cells  joined  in  parallel  send  through  the  same 
circuit?  What  current  will  one  such  cell  send  through  the  same  circuit? 

7.  Wrhat  current  will  the. 40  cells  in  parallel  send  through  an  am- 
meter which  has  a  resistance  of  .1  ohm  ?  What  current  would  the  40 
cells  in  series  send  through  the  same  ammeter?  What  current  would  a 
single  cell  send  through  the  same  ammeter  ? 

8.  Under  what  conditions  \vill  a  small  cell  give  practically  the  same 
current  as  a  large  one  of  the  same  type  ? 

9.  How  many  cells,  each  of  E.M.F.  1.5  volts  and  internal  resistance 
.2  ohm,  will  be  needed  to  send  a  current  of  at  least  1  ampere  through 
an  external  resistance  of  40  ohms  ? 

10.  Why  is  it  desirable  that  a  galvanometer  which  is  to  be  used  for 
measuring  currents  have  as  low  a  resistance  as  possible? 

11.  Ordinary  No.  9  telegraph  wire  has  a  resistance  of  20  ohms  to  the 
mile.    What  current  will  100  Daniell  cells  in  series,  each  of  E.M.F.  of 
1  volt,  send  through  100  miles  of  such  wire,  if  the  two  relays  have  a 
resistance  of  150  ohms  each  and  the  cells  an  internal  resistance  of  4 
ohms  each? 

12.  If  the  relays  of  the  preceding  problem  had  each  10,000  turns  of 
wire  in  their  coils,  how  many  ampere  turns  were  effective  in  magnetizing 
their  electromagnets  ? 

13.  If,  on  the  above  telegraph  line,  sounders  having  a  resistance  of 
3  ohms  each  and  500  turns  were  to  be  put  in  the  place  of  the  relays, 
how  many  ampere  turns  would  be  effective  in  magnetizing  their  cores  ? 
Why,  then,  does  the  electromagnet  of  the  relay  have  a  high  resistance  ? 

SECONDARY  CELLS 
338.  Lead  storage  batteries.    Let  two  6  by  8  inch  lead  plates  be 

screwed  to  a  half-inch  strip  of  some  insulating  material,  as  in  Fig.  291, 
and  immersed  in  a  solution  consisting  of  one  part  of  sulphuric  acid  to 
ten  parts  of  water.  Let  a  current  from  two  storage  or  three  dry  cells  in 
series,  C,  be  sent  through  this  arrangement,  an  ammeter  A  or  any 


282  ELECTEICITY  IX  MOTION 

low-resistance  galvanometer  being  inserted  in  the  circuit.  As  the  current 
flows,  hydrogen  bubbles  will  be  seen  to  rise  from  the  cathode  (the  plate 
at  which  the  current  leaves  the  solution),  while  the  positive  plate,  or 
anode,  will  begin  to  turn  dark  brown. 
At  the  same  time  the  reading  of  the 
ammeter  will  be  found  to  decrease  rap- 
idly. The  brown  coating  is  a  compound 
of  lead  and  oxygen,  called  lead  peroxide 
(PbO2),  which  is  formed  by  the  action 
upon  the  plate  of  the  oxygen  which  is  ^  ^  The  Q  Q£ 

liberated,  precisely  as  .in  the  experiment  the  gtorage  battery 

on  the  electrolysis  of  water  (§  302).  Now 

let  the  batteries  be  removed  from  the  circuit  by  opening  the  key  Kv 
and  let  an  electric  bell  B  be  inserted  in  their  place  by  closing  the  key 
K2.  The  bell  will  ring  and  the  ammeter  A  will  indicate  a  current  flowing 
in  a  direction  opposite  to  that  of  the  original  current.  This  current  will 
decrease  rapidly  as  the  energy  which  was  stored  in  the  cell  by  the  original 
current  is  expended  in  ringing  the  bell. 

This  experiment  illustrates  the  principle  of  the  storage  bat- 
tery. Properly  speaking,  there  has  been  no  storage  of  electricity, 
but  only  a  storage  of  chemical  energy. 

Two  similar  lead  plates  have  been  changed  by  the  action  of 
the  current  into  two  dissimilar  plates,  one  of  lead  and  one  of 
lead  peroxide ;  in  other  words,  an  ordinary  galvanic  cell  has 
been  formed,  for  any  two  dissimilar  metals  in  an  electrolyte 
constitute  a  primary  galvanic  cell.  In  this  case  the  lead  per- 
oxide plate  corresponds  to  the  copper  of  an  ordinary  cell,  and 
the  lead  plate  to  the  zinc.  This  cell  tends  to  create  a  current 
opposite  in  direction  to  that  of  the  charging  current ;  that  is, 
its  E.M.F.  pushes  back  against  the  E.M.F.  of  the  charging 
cells.  It  was  for  this  reason  that  the  ammeter  reading  fell. 
When  the  charging  current  is  removed,  this  cell  acts  exactly 
like  a  primary  galvanic  cell  and  furnishes  a  current  until  the 
thin  coating  of  peroxide  is  used  up.  The  only  important  differ- 
ence between  a  commercial  storage  cell  (Fig.  292)  and  the 
one  which  we  have  here  used  is  that  the  former  is  provided  in 


SECONDARY  CELLS 


283 


Fig.  292.   Lead-plate 
storage  cell 


the  making  with  a.  much  thicker  coat  of  the  "  active  material " 

(lead  peroxide  on  the  positive  plate  and  a  porous,  spongy 

lead  on  the  negative)  than  can  be  formed  by  a  single  charging 

such  as  we  used.  This  material  is  pressed 

into  interstices  in  the  plates,  as  shown 

in  Fig.  292.    The  E.M.F.  of  the  lead 

storage  cell  is  about  2  volts.    Since  the 

plates   are  always  very   close  together 

and  may  be  given  any  desired  size,  the 

internal  resistance  is  usually  small,  so 

that  the  currents  furnished  may  be  very 

large. 

The  usual  efficiency  of  the  lead  stor- 
age cell  is  about  75%  ;  that  is,  only 
about  ^  as  much  electrical  energy  can 
be  obtained  from  it  as  is  put  into  it. 

339.  Nickel-iron  storage  batteries.  Thomas  A.  Edison  (see 
opposite  p.  316)  developed  and  perfected  the  nickel-iron 
caustic-potash  storage  cell.  The  electrolyte  is  a  21%  solu- 
tion of  caustic  potash  in  water.  The  negative  plates  contain 
iron  powder  securely  retained  in  perforated  flat  rectangular 
capsules,  while  the  positive  plates  contain  oxide  of  nickel  in 
perforated  cylindrical  containers.  For  equal  capacities  the 
Edison  cell  weighs  about  half  as  much  as  the  lead  cell,  and 
it  will  stand  a  remarkable  amount  of  electrical  and  mechan- 
ical abuse.  The  E.M.F.  is  about  1.2  volts.  In  efficiency  it 
is  a  little  below  the  lead  cell.  Caustic  potash  is  now  replaced 
by  caustic  soda. 

QUESTIONS  AND  PROBLEMS 

1.  In  charging  a  storage  battery  is  it  better  to  say  that  the  current 
passes  into  the  cell  or  through  it  ?    What  is  "  stored  "  ? 

2.  The  lead  peroxide  plate  and  the  nickel  oxide  plate  are  both  called 
"  the  positives."   What  is  the  relation  of  the  charging  current  to  these 
plates  ? 


284  ELECTRICITY  IN  MOTION 

HEATING  EFFECTS  OF  THE  ELECTRIC  CURRENT 

340.  Heat  developed  in  a  wire  by  an  electric  current.   Let  the 
terminals  of  two  or  three  dry  cells  in  series  be  touched  to  a  piece  of 
No.  40  iron  or  German-silver  wire  and  the  length  of  wire  between  these 
terminals  shortened  to  -^  inch  or  less.   The  wire  will  be  heated  to  incan- 
descence and  probably  melted. 

The  experiment  shows  that  in  the  passage  of  the  current 
through  the  wire  the  energy  of  the  electric  current  is  trans- 
formed into  heat  energy.  The  electrical  energy  expended 
when  a  current  flows  between  points  of  given  P.D.  may  be 
spent  in  a  variety  of  ways.  For  example,  it  may  be  spent 
in  producing  chemical  separation,  as  in  the  charging  of  a 
storage  cell;  it  may  be  spent  in  doing  mechanical  work,  as 
is  the  case  when  the  current  flows  through  an  electric  motor ; 
or  it  may  be  spent  wholly  in  heating  the  wire,  as  was  the 
case  in  the  experiment.  It  will  always  be  expended  in  this 
last  way  when  no  chemical  or  mechanical  changes  are  pro- 
duced by  it.  (See  drawings  opposite  p.  269  for  uses  made 
of  heating  effects.) 

341.  Energy  relations  of  the  electric  current.     We  found 
in  Chapter  IX  that  energy  expended  on  a  water  turbine  is 
equal  to  the  quantity  of  water  passing  through  it  times  the 
difference  in  level  through  which  the  water  falls ;   or,  that 
the  power  (rate  of  doing  work)  is  the  product  of  the  fall  in 
level  and  the  current  strength.    In  just  the  same  way  it  is 
found  that  when  a  current  of  electricity  passes  through  a 
conductor,  the  power,  or  rate  of  doing  work,  is  equal  to  the 
fall  in  potential  between  the  ends  of 'the  conductor  times  the 
strength  of  the  electric  current.     If  the  P.D.  is  expressed  in 
volts  and  the  current  in  amperes,  the  power  is  given  in  watts, 
and  we  have          yoltg  x  ampereg  =  wattg_ 

The  energy  of  the  electric  current  is  usually  measured  in 
kilowatt  hours. 


HEATING  EFFECTS 


285 


A  kilowatt  hour  is  the  quantity  of  energy  furnished  in  one 
hour  ly  a  current  ivhose  rate  of  expenditure  of  energy  is  a 
kilowatt. 

342.  Incandescent  lamps.  The  ordinary  incandescent  lamp 
(Fig.  293)  consists  of  a  tungsten  filament  heated  to  incan- 
descence by  an  electric  current. 

Since  the  filament  would  burn  up  in  a  few  seconds  in  air, 
it  is  placed  in  a  highly  exhausted  bulb.  When  in  use  it 
slowly  vaporizes,  depositing  a  dark,  mirror- 
like  coating  of  metal  upon  the  inner  surface 
of  the  bulb.  The  lead-in  wires  are  sold- 
ered one  to  the  base  A  of  the  socket  and 
the  other  to  its  rim  J5,  these  being  the  elec- 
trodes through  which  the  current  enters  and 
leaves  the  lamp.  The  wires  ^#,  w,  sealed  into 
the  w^alls  of  the  bulb,  must  have  the  same 
coefficient  of  expansion  as  the  glass  to 
prevent  leakage  of  air. 

Incandescent  lamps  are  usually  grouped 
in  parallel  or  multiple,  on  a  circuit  that 
maintains  a  potential  of  something  over  100  volts  between 
the  terminals  of  the  lamps  (Fig.  318).  The  rate  of  consump- 
tion of  energy  is  about  1.25  watts  per  candle  power  for  the 
ordinary  sizes.  Tungsten  filaments,  being  operated  at  a  much 
higher  temperature  than  is  possible  with  the  now  almost 
obsolete  carbon  filament,  have  an  efficiency  nearly  three  times 
as  great. 

A  customer  usually  pays  for  his  light  by  the  kilowatt 
hour  (§  341).  The  rate  at  which  energy  is  consumed  by 
a  lamp  carrying  ^  ampere  at  100  volts  is  25  watts.  Two 
such  lamps  running  for  4  hours  would,  therefore,  consume 
2  x  4  x  25  =  200  watt  hours  =  .200  kilowatt  hour.  The 
energy  is  measured  and  recorded  on  a  recording  watt-hour 
meter  (Fig.  321). 


FIG.  293.   The  tung- 
sten vacuum  lamp 


286 


ELECTRICITY  IX  MOTION 


By  filling  the  bulb  with  nitrogen  a  very  efficient  form  of 
the  tungsten  lamp  is  obtained.  The  long  filament  is  wound 
into  an  exceedingly  fine  spiral  to  minimize  heat  radiation. 
As  we  have  already  learned  (§  207),  the  presence  of  gas 
retards  evaporation;  hence,  because  of  the  nitrogen  the  fila- 
ment may  be  raised  to  a  higher  temperature  than  is  permis- 
sible in  a  vacuum.  A  greatly  increased  candle  power  results 
from  the  slight  increase  in  current.  Moreover,  the  convection 
currents  in  the  gas-filled  lamp  cause  the  mir- 
ror due  to  vaporization  to  form  near  the  top 
of  the  globe,  where  it  does  not  obscure  the 
intensity  of  the  light.  The  larger  sizes  of 
gas-filled  lamps  consume  only  .6  watt  per 
candle  power. 

343.  The  arc  light.   When  two  carbon  rods  are 
placed  end  to  end  in  the  circuit  of  a  powerful  elec- 
tric generator,,  the  carbon  about  the  point  of  contact 
is  heated  red-hot.    If,  then,  the  ends  of  the  carbon 
rods  are  separated  one-fourth  inch  or  so,  the  current 
will  still  continue  to  flow,  for  a  conducting  layer  of 
incandescent  vapor,  called  an  electric  arc,  is  produced 
between  the  poles.     The  appearance  of  the  arc  is 
shown  in  Fig.  294.  At  the  +  pole  a  hollow,  or  crater, 
is  formed  in  the  carbon,  while  the  —  carbon  becomes 
cone-shaped,  as  in  the  figure.    The  carbons  are  con- 
sumed at  the  rate  of  about  an  inch  an  hour,  the  +  carbon  wasting  away 
about  twice  as  fast  as  the  —  one.    The  light  comes  chiefly  from  the  + 
crater,  where  the  temperature  is  about  3800°  C.,  the  highest  attainable 
by  man.   All  known  substances  are  volatilized  in  the  electric  arc. 

The  open  arc  requires  a  current  of  10  amperes  and  a  P.D.  between  its 
terminals  of  about  50  volts.  Such  a  lamp  produces  about  500  *  candle 
power,  and  therefore  consumes  energy  at  the  rate  of  about  1  watt  per 
candle  power.  The  light  of  the  arc  lamp  is  due  to  the  intense  heat 
developed  on  account  of  resistance,  not  to  actual  combustion,  or  burning. 
Nevertheless,  in  the  open  arc  the  oxygen  of  the  air  unites  so  rapidly  with 

*  This  is  the  so-called  "mean  spherical"  candle  power.  The  candle 
power  in  the  direction  of  maximum  illumination  is  from  1000  to  1200. 


FIG.  294.   The  arc 
light 


HEATING  EFFECTS 


287 


the  carbon  at  the  hot  tips  that  in  a  few  hours  the  rods  are  consumed. 
To  overcome  this  difficulty  the  inclosed  arc  (Fig.  295)  is  used.  Shortly 
after  the  arc  is  "  struck  "  the  oxygen  in  the  inner  globe  is  used  up  and 
then  the  hot  carbon  tips  are  surrounded  by  an 
atmosphere  of  carbon  dioxide  and  nitrogen. 
Under  these  conditions  the  carbons  last  130  to 
150  hours.  The  inclosed  arc  is  much  longer  than 
the  open  arc,  and  therefore  in  this  lamp  the  P.D. 
between  the  tips  is  greater,  usually  about  80  volts, 
while  the  rest  of  the  P.D.  of  the  line  is  taken  up 
in  the  resistance  coils  of  the  lamp. 

The  recently  invented  flaming  arc,  produced 
between  carbons  which  have  a  composite  core  con- 
sisting chiefly  of  carbon  and  fluoride  of  calcium, 
sometimes  reaches  an  efficiency  as  high  as  .27  watt 
per  candle  power.  It  gives 
an  excellent  yellow  light, 
which  penetrates  fog  well. 
344.  The  arc  light  auto- 
matic feed.  Since  the  two 
carbons  of  the  arc  gradually 
waste  away,  they  would  soon 
become  so  far  separated  that 
the  arc  could  no  longer  be 
maintained  were  it  not  for 
an  automatic  feeding  device 
which  keeps  the  distance  be- 
tween the  carbon  tips  very 

nearly  constant.    Fig.  296  shows  the  essential  fea- 
tures of  one  form  of  this  device.    When  no  current 
flows  through  the  lamp,  gravity  holds  the  carbon 
tips  at  e  together;  but  as  soon  as  the  current  is 
thrown  on,  it  energizes  the  magnet  coils  m,  m,  which 
draw  up  the  U-shaped  iron  core,  thus  striking  the 
arc  at  e.   As  the  carbons  slowly  waste  away,  the  arc 
becomes  longer,  the  resistance  greater,  and  the  cur- 
rent less;  hence   the  upward  magnetic  pull  weakens  and  the  upper 
carbon  descends,  and  vice  versa.    From  time  to  time  the  upper  carbon 
slips  down  through  the  friction  clutch  c.    It  is  clear,  therefore,  that  this 
automatic  device  will  maintain  that  particular  length  of  arc  for  which 


FIG.  295.    Mechanism 
of  a  direct-current  in- 
closed arc  lamp 


FIG.  296.    Feeding 
device  for  arc  lamp 


288 


ELECTRICITY  IN  MOTION 


equilibrium  exists  between  the  effect  of  gravity  pulling  down  and  mag- 
netism pulling  up.  A  dashpot  d,  containing  a  stationary  piston,  prevents 
the  magnetic  pull  from  suddenly  drawing  the  tips  at  e  too  far  apart. 

345.  The  Cooper-Hewitt  mercury  lamp.  The  Cooper-Hewitt  mercury 
lamp  (Fig.  297)  differs  from  the  arc  lamp  in  that  the  incandescent  body 
is  a  long  column  of  mercury  vapor  instead  of  an  incandescent  solid. 
The  lamp  consists  of 
an  exhausted  tube 
three  or  four  feet  long, 
the  positive  electrode 
at  the  top  consi  sting  of 
a  plate  of  iron,  while 
the  negative  electrode 
at  the  bottom  is  a 
small  quantity  of  mer- 
cury. Under  a  suf- 
ficient difference  of 
potential  between  these  terminals  a  long  mercury-vapor  arc  is  formed, 
which  stretches  from  terminal  to  terminal  in  the  tube.  This  arc  emits 
a  very  brilliant  light,  but  it  is  almost  entirely  wanting  in  red  rays.  The 
strength  of  its  actinic  rays  makes  it  especially  valuable  in  photography. 
Its  commercial  efficiency  is  about  .6  watt  per  candle  power.  Cooper- 
Hewitt  lamps  having  quartz  tubes  are  used  for  sterilizing  purposes 
because  of  the  powerful  ultra-violet  rays  which  the  quartz  transmits. 


FIG.  297.    The  Cooper-Hewitt  mercury-vapor 
arc  lamp 


QUESTIONS  AND  PROBLEMS 

1.  What  is  meant  by  a  104-volt  lamp?   What  would  happen  to  such 
a  lamp  if  the  P.D.  at  its  terminals  amounted  to  500  volts?    Trolley  cars 
are  usually  furnished  with  current  at  about  500  volts ;  how  would  you  use 
100-volt  lamps  on  such  a  circuit? 

2.  A  very  common  electric 
lamp    used    in    our    homes    is 
marked   25  watts    and   carries 
about  ^  ampere.    One  fresh  dry 
cell  on  short  circuit  will  deliver 
30  or  more  amperes.    Will  the 
cell  light  the  lamp? 

3.  A  50-vol6  carbon  lamp   carrying  1  ampere  has  about  the  same 
candle  power  as  a  100-volt  carbon  lamp  carrying  £  ampere.    Explain 
why. 


I 


FIG.  298 


HEATING  EFFECTS  289 

4.  If  a  storage  cell  has  an  E.M.F.  of  2  volts  and  furnishes  a  cur- 
rent of  5  amperes,  what  is  its  rate  of  expenditure  of  energy  in  watts? 

5.  Fig.  298  shows  the  connections  for  a  lamp  L  which  can  be 
turned  on  or  off  at  two  different  points  a  or  b.    Explain  how  it  works. 

6.  How  many  100-volt  lamps  each  carrying  ^  ampere  may  be  main- 
tained on  a  circuit  where  the  total  power  may  not  exceed  600  watts  ? 

7.  What  will  it  cost  to  use  an  electric  laundry  iron  for  6  hours  if  it 
takes  3.5  amperes  on  a  104-volt  circuit,  the  cost  of  current  being  $.09 
per  kilowatt  hour  ? 

8.  A  certain  electric  toaster  takes  5  amperes  at  110  volts.   It  will 
make  two  pieces  of  toast  at  once  in  3  minutes.    At  what  horse-power 
rate  does  the  toaster  convert  electrical  energy  into  heat  energy?    At 
$.08  per  kilowatt  hour  what  does  it  cost  to  make  12  pieces  of  toast? 

9.  How  many  lamps,  each  of  resistance  20  ohms  and  requiring  a 
current  of  .8  ampere,  can  be  lighted  by  a  dynamo  that  has  an  output 
of  4000  watts? 

10.  If  one  of  the  wire  loops  in  a  tungsten  lamp  is  short-circuited, 
what  effect  will  this  have  on  the  amount  of  current  flowing  through 
the  lamp?  on  the  brightness  of  the  filament? 

11.  How  many  cells  working  as  in  problem  4  would  be  equivalent 
to  1  H.P.  ?    (See  §  144,  p.  122.) 

12.  Since  one  calorie  is  equal  to  42,000,000  ergs,  1  watt  (10,000,000 
ergs  per  second)  develops  in  one  second  .24  calories.    Therefore  the 
number  of  calories,  H,  developed  in  t  seconds  by  a  current  of  /  amperes 
between  two  points  whose  P.D.  is  V  volts  is  expressed  by  the  equation 

H  =  I  x  V  x  t  x  .24. 

How  many  calories  per  minute  are  given  out  by  the  electric  toaster  of 
problem  8? 

13.  From  the  equation  of  problem  12  show  that 

H  =  PR  x  t  x  .24. 

14.  How  many  minutes  are  required  to  heat  600  g.  of  water  from 
15°  C.  to  100°  C.  by  passing  5  amperes  through  a  20-ohm  coil  immersed 
in  the  water? 

15.  Why  is  it  possible  to  get  a  much  larger  current  from  a  storage 
cell  than  from  a  Daniell  cell  ? 

16.  If  an  automobile  is  equipped  with  6-volt  lamps,  how  many  lead 
storage  cells  must  be  on  the  car?    Are  these  cells  in  series  or  multiple? 

17.  A  small  arc  lamp  requires  a  current  of  5  amperes  and  a  difference 
of  potential  between  its  terminals  of  45  volts.    What  resistance  must  be 
connected  in  series  with  it  in  order  to  use  it  on  a  110-volt  circuit? 


CHAPTER  XY 

INDUCED  CURRENTS 
THE   PRINCIPLE   OF  THE   DYNAMO    AND   MOTOR 

346.  Current  induced  by  a  magnet.  Let  400  or  500  turns  of 
No.  22  copper  wire  be  wound  into  a  coil  C  (Fig.  299)  about  two  and  a 
half  inches  in  diameter.  Let  this  coil  be  connected  into  circuit  with 
a  lecture-table  galvanometer  (Fig.  263),  or  even  a  simple  detector  made 
by  suspending  in  a  box, 
with  No.  40  copper  wire, 
a  coil  of  200  turns  of  No. 
30  copper  wire  (see  Fig. 
299).  Let  the  coil  C  be  S[ 
thrust  suddenly  over  the 
N  pole  of  a  strong  horse- 
shoe magnet.  The  deflec-  FlG  299  Induction  of  electric  currents 
tion  of  the  pointer  p  of  by  magnets 

the  galvanometer  will  in- 
dicate a  momentary  current  flowing  through  the  coil.  Let  the  coil  be 
held  stationary  over  the  magnet.  The  pointer  will  be  found  to  come  to 
rest  in  its  natural  position.  Now  let  the  coil  be  removed  suddenly  from 
the  pole.  The  pointer  will  move  in  a  direction  opposite  to  that  of  its 
first  deflection,  showing  that  a  reverse  current  is  now  being  generated 
in  the  coil. 

We  learn,  therefore,  that  a  current  of  electricity  may  be 
induced  in  a  conductor  by  causing  the  latter  to  move  through  a 
magnetic  field,  while  a  magnet  has  no  such  influence  upon  a 
conductor  which  is  at  rest  with  respect  to  the  field.  This  •dis- 
covery, one  of  the  most  important  in  the  history  of  science, 
was  announced  by  the  great  Faraday  in  1831.  From  it  have 
sprung  directly  most  of  the  modern  industrial  developments 
of  electricity. 

290 


MICHAEL  FARADAY  (1791-1867) 

Famous  English  physicist  and  chemist ;  one  of  the  most  gifted  of  experimenters 
son  of  a  poor  blacksmith ;  apprenticed  at  the  age  of  thirteen  to  a  London  book- 
binder, with  whom  he  worked  nine  years ;  applied  for  a  position  in  Sir  Humphry 
Davy's  laboratory  at  the  Royal  Institution  in  1813 ;  became  director  of  this  labo- 
ratory in  1825;  discovered  electromagnetic  induction  in  1831;  made  the  first 
dynamo;  discovered  in  1833  the  laws  of  electrolysis,  now  known  as  Faraday's 
laws ;  the  farad,  the  practical  unit  of  electrical  capacity,  is  named  in  his  honor 


INDUCTION  MOTOR 

One  of  the  most  familiar  of  the  more  recent  applications  of  the  great  principle  of 
induction  discovered  by  Faraday  is  the  induction  motor,  which  has  come  into 
extensive  use  in  both  large  and  small  sizes.  The  particular  one  here  shown  is 
known  as  the  squirrel-cage  form,  in  which  there  is  no  electrical  connection 
between  the  stator  (the  stationary  part)  and  the  rotor  (the  revolving  part) .  The 
stator  is  wound  on  a  laminated  core  like  the  stator  of  a  dynamo,  while  the  rotor 
consists  of  copper  bars  laid  in  a  slotted  laminated  core,  their  ends  being  joined  to 
copper  rings,  one  at  each  end.  The  bars  are  therefore  in  parallel.  The  alternating 
current  applied  to  the  stator  windings  develops  a  magnetic  field  which  rotates 
around  the  iron  ring  of  the  stator.  This  is  equivalent  to  a  set  of  magnetic  poles 
mechanically  rotated  around  the  rotor.  The  magnetic  lines  of  force  which  there- 
fore cut  across  the  copper  bars  of  the  rotor  generate  in  them  an  E.M.F.  which 
causes  a  current  to  flow  in  the  copper  system  of  the  rotor.  The  rotating  field 
reacts  with  the  field  produced  by  the  current  in  the  conductors  of  the  rotor  so  as 
to  cause  the  rotor  to  be  dragged  around  after  the  rotating  field 


PRINCIPLE  OF  THE  DYNAMO  AND  MOTOR     291 


347.  Direction  of  induced  current.    Lenz's  law.    In  order  to 

find  the  direction  of  the  induced  current,  let  a  very  small  P.D.  from  a 
galvanic  cell  be  applied  to  the  terminals  A  and  B  (Fig.  299),  and  note 
the  direction  in  which  the  pointer  moves  when  the  current  enters,  say, 
at  A.  This  will  at  once  show  in  what  direction  the  current  was  flow- 
ing in  the  coil  C  when  it  was  being  thrust  over  the  N  pole.  By  a  simple 
application  to  C  of  the  right-hand  rule  (§  308)  we  can  then  tell  which 
was  the  N  and  which  the  £  face  of  the  coil  when  the  induced  current 
was  flowing  through  it.  In  this  way  it  will  be  found  that  if  the  coil  wTas 
being  moved  past  the  N  pole  of  the  magnet,  the  current  induced  in  it 
was  in  such  a  direction  as  to  make  the  lower  face  of  the  coil  an  N  pole 
during  the  downward  motion  and  an  S  pole  during  the  upward  motion. 
In  the  first  case  the  repulsion  of  the  N  pole  of  the  magnet  and  the  N 
pole  of  the  coil  tended  to  oppose  the  motion  of  the  coil  while  it  was 
moving  from  a  to  b,  and  the  attraction  of  the  N  pole  of  the  magnet  and 
the  S  pole  of  the  coil  tended  to  oppose  the  motion  while  it  was  moving 
from  b  to  c.  In  the  second  case  the  repulsion  of  the  two  N  poles  tended 
to  oppose  the  motion  between  b  and  c,  and  the  attraction  between  the 
N  pole  of  the  magnet  and  the  S  pole  of  the  coil  tended  to  oppose  the 
upward  motion  from  b  to  a.  In  every  case,  therefore)  the  motion  is  made 
against  an  opposing  force. 

From  these  experiments,  and  others  like  them,  we  arrive  at 
the  following  law :  Wfenever  a  current  is  induced  by  the  rela- 
tive motion  of  a  magnetic  field  and  a  conductor,  the  direction  of 
the  induced  current  is  always  such  as  to  set  up  a  magnetic  field 
which  opposes  the  motion.  This  is  Lenz's  law. 
This  law  might  have  been  predicted  at  once 
from  the  principle  of  the  conservation  of 
energy  ;  for  this  principle  tells  us  that  since 
an  electric  current  possesses  energy,  such 
•  a  current  can  appear  only  through  the  ex- 
penditure of  mechanical  work  or  of  some  FIG.  300. 
other  form  of  energy. 

348.  Condition  necessary  for  an  induced 
E.M.F.     Let  the   coil  be   held   in  the   position 

shown  in  Fig.  300,  and  moved  back  and  forth  parallel  to  the  magnetic 
field,  that  is,  parallel  to  the  line  NS.    No  current  will  be  induced. 


Currents 
induced  only  when 
conductor  cuts  lines 
of  force 


292 


INDUCED  CURRENTS 


FIG.  301.  E.M.F. 
induced  when  a 
straight  conductor 
cuts  magnetic  lines 


By  experiments  of  this  sort  it  is  found  that  an  E.M.F.  is 
induced  in  a  coil  only  when  the  motion  takes  place  in  such  a  way 
as  to  change  the  total  number  of  magnetic  lines 
of  force  which  are  inclosed  by  the  coil.  Or,  to 
state  this  rule  in  more  general  form,  an 
E.M.F.  is  induced  in  any  element  of  a  con- 
ductor when,  and  only  when,  that  element  is 
moving  in  such  a  way  as  to  cut  magnetic 
lines  of  force.* 

It  will  be  noticed  that  the  first  statement 
of  the  rule  is  included  in   the  second,  for 
whenever  the  number  of  lines  of  force  which 
pass  through  a  coil  changes,  some  lines  of  force  must  cut 
across  the  coil  from  the  inside  to  the  outside,  or  vice  versa. 

349.  The  principle  of  the  electric  motor. 
Let  a  vertical  wire  ab  be  rigidly  attached  to  a 
horizontal  wire  gh,  and  let  the  latter  be  supported 
by  a  ring  or  other  metallic  support,  in  the  manner 
shown  in  Fig.  302,  so  that  ab  is  free  to  oscillate 
about  gh  as  an  axis.  Let  the  lower  end  of  ab  dip 
into  a  trough  of  mercury.  When  a  magnet  is  held 
in  the  position  shown  and  a  current  from  a  dry  cell 
is  sent  down  through  the  wire,  the  wire  will  in- 
stantly move  in  the  direction  indicated  by  the 
arrow  f,  namely,  at  right  angles  to  the  direction  of 
the  lines  of  magnetic  force.  Let  the  direction  of 
the  current  in  the  wire  be  reversed.  The  direction 
of  the  force  acting  on  the  wire  will  be  found  to  be 
reversed  also. 

We  learn,  therefore,  that  a  wire  carrying 
a  current  in  a  magnetic  field  tends  to  move  in 

*  If  a  strong  electromagnet  is  available,  these  experiments  are  more  instruc- 
tive if  performed,  not  with  a  coil,  as  in  Fig.  300,  but  with  a  straight  rod 
(Fig.  301)  to  the  ends  of  which  are  attached  wires  leading  to  a  galvanometer. 
Whenever  the  rod  moves  parallel  to  the  lines  of  magnetic  force  there  will 
be  no  deflection,  but  whenever  it  moves  across  the  lines  the  galvanometer 
needle  will  move  at  once. 


FIG.  302.   The  prin- 
ciple of  the  electric 
motor 


PRINCIPLE  OF  THE  DYNAMO  AND  MOTOR     293 


a  direction  at  right  angles  both  to  the  direction  of  the  field  and 
to  the  direction  of  the  current.  This  fact  underlies  the  opera- 
tion of  all  electric  motors. 

350.  The  motor  and  dynamo  rules.  A  convenient  rule  for 
determining  whether  the  wire  ab  (Fig.  302)  will  move  forward 
or  back  in  a  given  case  may  be  obtained  as  follows:  If  the 
field  of  a  magnet  alone  is  represented  by  Fig.  303,  and  that 
due  to  the  current  *  alone  by  Fig.  304,  then  the  resultant  field 
when  the  current-bearing  wire  is  placed  between  the  poles  of 
the  magnet  is  that  shown  in  Fig.  305 ;  for  the  strength  of  the 


FIG.  303.   Field  of 
magnet  alone 


FIG.  304.    Field  of 
current  alone 


FIG.  305.  Field  of  magnet 
and  current 


field  above  the  wire  is  now  the  sum  of  the  two  separate  fields, 
while  the  strength  below  it  is  their  difference.  Now  Faraday 
thought  of  the  lines  of  force  as  acting  like  stretched  rubber 
bands.  This  would  mean  that  the  wire  in  Fig.  305  would  be 
pushed  down.  Whether  the  lines  of  force  are  so  conceived  or 
not,  the  motor  rule  may  be  stated  thus : 

A  current  in  a  magnetic  field  tends  to  move  away  from  the 
side*  on  which  its  lines  are  added  to  those  of  the  field. 

The  dynamo  rule  follows  at  once  from  the  motor  rule  and 
Lenz's  law.  Thus,  when  a  wire  is  moved  through  a  magnetic 
field  the  current  induced  in  it  must  be  in  such  a  direction  as 

*  The  cross  in  the  conductor  of  Fig.  304,  representing  the  tail  of  a  retreat- 
ing arrow,  is  to  indicate  that  the  current  flows  away  from  the  reader.  A  dot, 
representing  the  head  of  an  advancing  arrow,  indicates  a  current  flowing 
toward  the  reader. 


294  INDUCED  CURRENTS 

to  oppose  the  motion ;  therefore  the  induced  current  will  be 
in  such  a  direction  as  to  increase  the  number  of  lines  on  the  side 
toward  which  it  is  moving. 

351.  Strength  of  the  induced  E.M.F.    The  strength  of  an 
induced  E.M.F.  is  found  to  depend  simply  upon  the  number  of 
lines  of  force  cut  per  second  by  the  conductor,  or,  in  the  case 
of  a  coil,  upon  the  rate  of  change  in  the  number  of  lines  of 
force  which  pass  through  the  coil.    The  strength  of  the  current 
which  flows  is  then  given  by  Ohm's  law ;  that  is,  it  is  equal  to 
the  induced  E.M.F.  divided  by  the  resistance  of  the  circuit. 
The  number  of  lines  of  force  which  the  conductor  cuts  per 
second  may  always  be  determined  if  we  know  the  velocity  of 
the  conductor  and  the  strength  of  the  magnetic  field  through 
which  it  moves.    For  it  will  be  remembered  that,  according  to 
the  convention  of  §  270,  a  field  of  unit  strength  is  said  to  con- 
tain one  line  of  force  per  square  centimeter,  a  field  of  1000 
units  strength  1000  lines  per  square  centimeter,  etc.    In  a 
conductor  which  is  cutting  lines  at  the  rate  of  100,000,000 
per  second  there  is  an  induced  E.M.F.  of  1  volt.  *    The  reason 
why  we  used  a  coil  of  500  turns  instead  of  a  single  turn  in  the 
experiment  of  §  346  was  that  by  thus  making  the  conductor 
in  which  the  current  was  to  be  induced  cut  the  lines  of  force 
of  the  magnet  500  times  instead  of  once,  we  obtained  500 
times  as  strong  an  induced  E.M.F.,  and  therefore  500  times 
as  strong  a  current  for  a  given  resistance  in  the  circuit. 

352.  Currents  induced  in  rotating  coils.    Let  a  400-  or  500-tum 
coil  of  No.  28  copper  wire  be  made  small  enough  to  rotate  between  the 
poles  of  a  horseshoe  magnet,  and  let  it  be  connected  into  the  circuit  of 
a  galvanometer,  precisely  as  in  §  346.    Starting  with  the  coil  in  the  posi- 
tion of  Fig.  306,  (1),  let  it  be  rotated  suddenly  clockwise  (looking  down 
from  above)  through  180°.    A  strong  deflection  of  the  galvanometer  will 
be  observed.  Let  it  be  rotated  through  the  next  180°  back  to  the  starting 
point.    An  opposite  deflection  will  be  observed. 

*  This  may  be  considered  as  the  scientific  definition  of  the  volt,  convenience 
alone  having  dictated  the  legal  definition  given  in  §  334. 


PRINCIPLE  OF  THE  DYNAMO  AND  MOTOR     295 


(l) 


FIG.  306.     Direction  of   cur- 
rents induced  in  a  coil  rotat- 
ing in  a  magnetic  field 


The  arrangement  is  a  dynamo  in  miniature.  During  the 
first  half  of  the  revolution  (see  Fig.  306,  (2))  the  wires  on 
the  right  side  of  the  loop  were  cutting  the  lines  of  force  in  one 
direction,  while  the  wires  on  the  left 
side  were  cutting  them  in  the  oppo- 
site direction.  A  current  was  being 
generated  down  on  the  right  side 
of  the  coil  and  up  on  the  left  side 
(see  dynamo  rule).  It  will  be  seen 
that  both  currents  flow  around  the 
coil  in  the  same  direction.  The  in- 
duced current  is  strongest  when  the 
coil  is  in  the  position  shown  in 
Fig.  306,  (2),  because  there  the 
lines  of  force  are  being  cut  most  rapidly.  Just  as  the  coil  is 
moving  into  or  out  of  the  position  shown  in  Fig.  306,  (1), 
its  edges  are  moving  parallel  to  the  lines  of  force,  and  hence 
no  current  is  induced,  since  no  lines  of  force  are  being  cut 
As  the  coil  moves  through  the  last  180°  of  its  revolution 
both  sides  are  cutting  the  same  lines  of  force  as  before,  but 
they  are  cutting  them  in  an  opposite  direction ;  hence  the 
current  generated  during  this  last  half  is  opposite  in  direction 
to  that  of  the  first  half.* 

QUESTIONS  AND  PROBLEMS 

1.  Can  the  number  of  lines  of  force  within  a  closed  coil  of  wire  be 
increased  or  decreased  without  the  lines  being  cut  by  the  wire  ?  Explain. 

2.  Under  what  conditions  may  an  electric  current  be  produced  by  a, 
magnet  ? 

3.  How  many  lines  of  force  must  be  cut  per  second  to  induce  10  volts? 

4.  If  a  coil  of  wire  is  rotated  about  a  vertical  axis  in  the  earth's  field> 
an  alternating  current  is  set  up  in  it.    In  what  position  is  the  coil  when 
the  current  changes  direction? 

*A  laboratory  experiment  on  the  principles  of  induction  should  be 
performed  at  about  this  point.  See,  for  example,  Experiment  36  of  the 
authors'  Manual. 


296 


INDUCED  CURRENTS 


5.  State  Lenz's  law,  and  show  how  it  follows  from  the  principle  of 
the  conservation  of  energy. 

6.  A  coil  is  thrust  over  the  S  pole  of  a  magnet.    Is  the  direction  of 
the  induced  current  clockwise  or  counterclockwise  as  you  look  down 
upon  the  pole  ? 

7.  A  ship  having  an  iron  mast  is  sailing  east.    In  what  direction  is 
the  E.M.F.  induced  in  the  mast  by  the  earth's  magnetic  field?    If  a  wire 
is  brought  from  the  top  of  the  mast  to  its  bottom,  no  current  will  flow 
through  the  circuit.    Why? 

8.  A  current  is  flowing  from  top  to  bottom  in  a  vertical  wire.    In 
what  direction  will  the  wire  tend  to  move  on  account  of  the  earth's 
magnetic  field? 

DYNAMOS 

353.  A  simple  alternating-current  dynamo.  The  simplest 
form  of  commercial  dynamo  consists  of  a  coil  of  wire  so 
arranged  as  to  rotate  continuously  between  the  poles  of 
a  powerful  electromagnet 
(Fig.  307). 

In  order  to  make  the  mag- 
netic field  in  which  the  con- 
ductor is  moved  as  strong  as 
possible,  the  coil  is  wound 
upon  an  iron  core  C.  This 
greatly  increases  the  total 
number  of  lines  of  magnetic 
force  which  pass  between  JV 
and  S,  for  instead  of  an  air 
path  the  core  offers  an  iron 
path,  as  shown  in  Fig.  308. 

The  rotating  part,  consisting  of  the  coil  with  its  core,  is 
called  the  armature.  One  end  of  the  coil  is  attached  to  the 
insulated  metal  ring  R,  which  is  attached  rigidly  to  the  shaft 
of  the  armature  and  therefore  rotates  with  it,  while  the  other 
end  of  the  coil  is  attached  to  a  second  ring  R'.  The  brushes 
b  and  V,  which  constitute  the  terminals  of  the  external  circuit, 
are  always  in  contact  with  these  rings. 


FIG.  307.    Drum-wound  armature 


DYNAMOS 


297 


As  the  coil  rotates,  an  induced  alternating  current  passes 
through  the  circuit.  This  current  reverses  direction  as  often 
as  the  coil  passes  through  the 
position  shown  in  Fig.  308,  that 
is,  the  position  in  which  the  con- 
ductors are  moving  parallel  to 
the  lines  of  force ;  for  at  this 
instant  the  conductors  which  were 
moving  up  begin  to  move  down, 
and  those  which  were  moving 
down  begin  to  move  up.  The  cur- 
rent reaches  its  maximum  value 
when  the  coils  are  moving  through  a  position  90°  farther  on, 
for  then  the  lines  of  force  are  being  cut  most  rapidly  by  the 
conductors  OR-  both  sides  of  the  coil.  These  facts  are  graphi- 
cally represented  by  the  curve  of  E.M.F.'s  (Fig.  309). 

354.  The  multipolar  alternator.  For  most  commercial  purposes  it  is 
found  desirable  to  have  120  or  more  alternations  of  current  per  second. 
This  could  not  be  attained  easily  with  two-pole  machines  like  those 


FIG.  308.   End  view  of  drum 
armature 


0° 


90° 


270 


etc. 


FIG.  309.    Curve  of  alternating  electromotive  force 

sketched  in  Figs.  307  and  308.  Hence  commercial  alternators  are 
usually  built  with  a  large  number  of  poles  alternately  N  and  S,  arranged 
around  the  circumference  of  a  circle  in  the  manner  shown  in  Fig.  310. 
These  poles  are  excited  by  a  direct  current.  The  dotted  lines  represent 
the  direction  of  the  lines  of  force  through  the  iron.  It  will  be  seen  that 
the  coils  which  are  passing  beneath  N  poles  have  induced  currents  set 
up  in  them  the  direction  of  which  is  opposite  to  that  of  the  currents 
which  are  induced  in  the  conductors  which  are  passing  beneath  the  S 
poles.  Since,  however,  the  direction  of  winding  of  the  armature  coils 
changes  between  each  two  poles,  all  the  inductive  effects  of  all  the  poles 
are  added  in  the  coil  and  constitute  at  any  instant  one  single  current 


298 


INDUCED  CURRENTS 


flowing  around  the  complete  circuit  in  the  manner  indicated  by  the 
arrows  in  the  diagram.    This  current  reverses  direction  at  the  instant 
at  which  all  the  coils  pass  the  midway  points  between  the  JV  and  S  poles. 
The  number   of   alternations  per 
second  is  equal  to  the  number  of 
poles  multiplied  by  the  number  of 
revolutions  per  second.    The  field 
magnets  ,/Vand  S  of  such  a  dynamo 
are    usually    excited    by    a  direct 
current  from   some  other   source. 
Fig.  311  represents  an  alternating- 
current    dynamo    with    revolving 
field  and  stationary  armature  con- 
nected directly  to  a  tandem  com- 
pound engine.  Alternators  of  5000- 
kilowatt    capacity     (nearly    7000        FIG.  310.   Diagram  of  alternating- 
horse  power)  have  been  built  to  current  dynamo 
run  at  the  unusually  high  speed 

of  3600  revolutions  per  minute.    Alternators  of  lower  speed  but  of  very 
much  greater  capacity  are  common   (see  huge  rotor  opposite  p.  257). 

355.  The  principle  of  the  commutator.    By  the  use  of  a  so- 
called  commutator  it  is  possible  to  transform  a  current  which 


FK;  .311.    Alternating-current  dynamo 

is  alternating  in  the  coils  of  the  armature  to  one  which  always 
flows  in  the  same  direction  through  the  external  portion  of 
the  circuit.  The  simplest  possible  form  of  such  a  commutator 


DYNAMOS 


299 


FIG.  312.   The  simple  commutator 


is  shown  in  Fig.  312.    It  consists  of  a  single  metallic  ring 

which  is  split  into  two  equal  insulated  semicircular  segments 

a  and  c.     One  end  of  the  ro- 

tating coil  is  soldered  to  one 

of   these   semicircles,  and   the 

other  end  to  the   other  semi- 

circle.   Brushes   b   and   b!  are 

set  in  such  positions  that  they 

lose  contact  with  one  semicircle 

and   make    contact    with    the 

other  at  the  instant  at  which 

the  current  changes  direction  in  the  armature.    The  current, 

therefore,  always  passes  out  to  the  external  circuit  through 

the   same  brush.    While  a  cur- 

rent from  such  a  coil  and  com- 

mutator  as   that  shown  in  the 

figure  would  always  flow  in  the 

same  direction  through  the  ex- 

ternal circuit,  it  would  be  of  a 

pulsating  rather   than  a  steady 

character,  for  it  would  rise  to  a 

FIG.  313.  Two-pole  direct-current 

maximum  and  fall  again  to  zero  dynamo  with  ring  armature 

twice  during  each  complete  revo- 

lution of  the  armature.  This  effect  is  avoided  in  the  com- 
mercial direct-current  dynamo  by  building  a  commutator  of 
a  large  number  of  segments  instead  of  two,  and  connecting 


0°  90°          180°          270°        360°         etc. 

FIG.  314.    Curve  of  commutated  electromotive  force 

each  to  a  portion  of  the  armature  coil  in  the  manner  shown 
in  Fig.  313.  The  result  of  using  a  simple  split-ring  com- 
mutator is  shown  graphically  in  Fig.  314. 


300 


INDUCED  CURRENTS 


FIG.  315.    The  direct-current 
dynamo,  drum  winding 


356.  The  drum-armature  direct-current  dynamo.  Fig.  315  is  a  diagram 
illustrating  the  construction  of  a  commercial  two-pole  direct-current 
dynamo  of  the  drum-armature  type. 
At  a  given  instant  currents  are  being 
induced  in  the  same  direction  in  all 
the  conductors  on  the  left  half  of  the 
armature.  The  cross  on  these  conduc- 
tors, representing  the  tail  of  a  retreat- 
ing arrow,  is  to  indicate  that  these 
currents  flow  away  from  the  reader. 
No  E.M.F.'s  are  induced  in  the  con- 
ductors at  the  top  and  bottom  of  the 
armature,  where  the  motion  is  parallel 
to  the  magnetic  lines.  On  the  right 
half  of  the  ring,  on  the  other  hand,  the  induced  currents  are  all  in  the 
opposite  direction,  that  is,  toward  the  reader,  since  the  conductors  are 
here  all  moving  up  instead  of  down.  The  dot  in  the  middle  of  these 
conductors  represents  the 
head  of  an  approaching 
arrow.  It  will  be  seen,  how- 
ever, in  tracing  out  the  con- 
nections 1, 11?  2, 2P  3, 3r  etc., 
of  Fig.  315  (the  dotted  lines 
representing  connections  at 
the  back  of  the  drum),  that 
the  coil  is  so  wound  about 
the  drum  that  the  currents 
in  both  halves  are  always 
flowing  toward  one  brush  b, 
from  which  they  are  led  to 
the  external  circuit  and  back 
at  T)'.  This  condition  always 
exists,  no  matter  how  fast  pIG 

the  rotation;  for  it  will  be 
seen  that  as  each  loop  ro- 
tates into  the  position  where  the  direction  of  its  current  reverses,  it 
passes  a  brush  and  therefore  at  once  becomes  a  part  of  the  circuit  on 
the  other  half  of  the  drum  where  the  currents  are  all  flowing  in  the 
opposite  direction.  Fig.  316  shows  a  typical  modern  four-pole  generator, 
and  Fig.  317  the  corresponding  drum-wound  armature.  Fig.  326  (p.  310) 


A  four-pole  direct-current 
generator 


DYNAMOS 


301 


Main  Circuit 


illustrates  nicely  the  method  of  winding  such  an  armature,  each  coil 
beginning  on  one  segment  of  the  commutator  and  ending  on  the 
adjacent  segment. 

357.  Dynamo  lighting  circuit.  The 
type   of   circuit   generally  used   in 
B.C.  incandescent  lighting  is  shown 
in  Fig.  318.  The  lamps  are  arranged 
in  parallel  between  the  mains.   The 

field  magnets  are  excited  partly  by     FIG.  31 7.  A  modern  drum  armature 

a  few  series  turns  which  carry  the 

whole  current  going  to  the  lamps,  and  partly  by  a  shunt  coil  consisting 

of  many  turns  of  fine  wire  (Fig.  318).    This  combination  of  series  and 

shunt  winding  maintains  the  P.D.  across  the 

mains  constant  for  a  great  range  of   loads. 

Such  a  machine  is  called  a  compound  wound 

dynamo,  to  distinguish  it  from  a  series  wound 

machine,  for  example,  which  dispenses  with 

the  shunt  coil.  • 

In  all  self-exciting  machines  there  is 
enough  residual  magnetism  left  in  the  iron 
cores  after  stopping  to  start  feeble  induced 
currents  when  started  up  again.  These  cur- 
rents immediately  increase  the  strength  of  the 
magnetic  field,  and  so  tjie  machine  quickly 

builds  up  its  current  until  the  limit  of  mag-  FlG-  318-  The  compound- 
netization  is  reached.  wound  dynamo 

358.  The  electric  motor.    In  construction  the  electric  motor 
differs  in  no  essential  respect  from  the  dynamo.    To  analyze 
the  operation  as  a  motor  of  such  a  machine  as  that  shown  in 
Fig.  313,  suppose  a  current  from  an  outside  source  is1  first  sent 
around  the  coils  of  the  field  magnets  and  then  into  the  arma- 
ture at  bf.    Here  it  will  divide  and  flow  through  all  the  con- 
ductors  on  the  left  half  of  the  ring  in  one  direction,  and 
through  all  those  on  the  right  half  in  the  opposite  direction. 
Hence,  in  accordance  with  the  motor  rule,  all  the  conductors 
on  the  left  side  are  urged  upward  by  the  influence  of  the 
field,  and  all  those  on  the  right  side  are  urged  downward. 
The  armature  will  therefore  begin  to  rotate,  and  this  rotation 


302 


INDUCED  CURRENTS 


will  continue  as  long  as  the  current  is  sent  in  at  br  and  out 
at  b;  for  as  fast  as  coils  pass  either  b  or  br  the  direction 
of  the  current  flowing  through  them  changes,  and  therefore 
the  direction  of  the  force  acting  on  them  changes.  The  left 
half  is  therefore  always  urged  up  and  the  right  half  down. 
The  greater  the  strength  of  the  current,  the  greater  the  force 
acting  to  produce  rotation. 

If  the  armature  is  of  the  drum  type  (Fig.  315),  the  con- 
ditions are  not  essentially  different;  for,  as  may  be  seen  by 
following  out  the  windings,  the  current  entering  at  b'  will 
flow  through  all  the  conductors  on  the  left  half  in  one  direction 
and  through  those 
on  the  right  half  in 
the  opposite  direc- 
tion. The  commu- 
tator keeps  these 
conditions  always 
fulfilled.  The  induc- 
tion motor  is  pictured 
and  described  oppo- 


FIG.  319.    Railway  motor,  upper  field  raised 


site  page  291. 

The  electric  motor 
is  a  device  which  receives  electrical  energy  and  converts  it 
into  mechanical  energy.  The  dynamo  is  a  device  which  re- 
ceives mechanical  energy  from  a  steam  engine,  water  wheel, 
or  other  source  and  converts  it  into  electrical  energy, 

359.  Street-car  motors.  Electric  street  cars  are  nearly  all  operated 
by  direct-current  series-wound  motors  placed  under  the  cars  and  attached 
by  gears  to  the  axles.  Fig.  319  shows  a  typical  four-pole  street-car  motor. 
The  two  upper  field  poles  are  raised  with  the  case  when  the  motor  is 
opened  for  inspection,  as  in  the  figure.  The  current  is  generally  supplied 
by  compound-wound  dynamos  which  maintain  a  constant  potential  of 
about  500  volts  between  the  trolley  or  third  rail  and  the  track  which 
is  used  as  the  return  circuit.  The  cars  are  always  operated  in  parallel, 
as  shown  in  Fig.  320.  In  a  few  instances  street  cars  are  operated  upon 


DYNAMOS  303 

alternating,  instead  of  upon  direct-current,  circuits.  In  such  cases  the 
motors  are  essentially  the  same  as  direct-current  series-wound  motors ; 
for  since  in  such  a  machine  the  current  must  reverse  in  the  field  magnets 
at  the  same  time  that  it  reverses  in  the  armature,  it  will  be  seen  that 

Trolley  Wire  or  3d  Rail 


1 

nnnnnnnnj  1 

DDDDDI 

at  Power  V     > 
1                Station   »>C 

y=m—  rm«            \ 

L)             O  '  — 

Track 
FIG.  320.    Street-car  circuit 

the  armature  is  always  impelled  to  rotate  in  one  direction,  whether  it 
is  supplied  with  a  direct  or  with  an  alternating  current.  Other  types  of 
A.C.  motors  are  not  well  adapted  to  starting  with  full  load. 

360.  Back  E.M.F.  in  motors.  When  an  armature  is  set  into 
rotation  by  sending  a  current  from  some  outside  source  through 
it,  its  coils  move  through  a  magnetic  field  as  truly  as  if  the 
rotation  were  produced  by  a  steam  engine,  as  is  the  case  in 
running  a  dynamo.  An  induced  E.M.F.  is  therefore  set  up 
by  this  rotation.  In  other  words,  while  the  machine  is  acting 
as  a  motor  it  is  also  acting  as  a  dynamo.  The  direction  of  the 
induced  E.M.F.  due  to  this  dynamo  effect  will  be  seen,  from 
Lenz's  law  or  from  a  consideration  of  the  dynamo  and  motor 
rules,  to  be  opposite  to  the  outside  P.D.,  which  is  causing 
current  to  pass  through  the  motor.  The  faster  the  motor  rotates, 
the  faster  the  lines  of  force  are  cut,  and  hence  the  greater  the 
value  of  this  so-called  lack  E.M.F.  If  the  motor  were  doing 
no  work,  the  speed  of  rotation  would  increase  until  the  back 
E.M.F.  reduced  the  current  to  a  value  simply  sufficient  to 
overcome  friction.  It  will  be  seen,  therefore,  that,  in  general, 
the  faster  the  motor  goes,  the  less  the  current  which  passes 
through  its  armature,  for  this  current  is  always  due  to  the 
difference  between  the  P.D.  applied  at  the  brushes  —  500  volts 
in  the  case  of  trolley  cars  —  and  the  back  E.M.F.  When  the 


304 


INDUCED  CURRENTS 


motor  is  starting,  the  back  E.M.F.  is  zero  ;  and  hence,  if  the  full 
500  volts  were  applied  to  the  brushes,  the  current  sent  through 
would  be  so  large  as  to  ruin  the  armature  through  overheating. 
To  prevent  this  motors  are  furnished  with  a  starting  box,  con- 
sisting of  resistance  coils  which  are  thrown  into  series  with 
the  motor  on  starting,  and  thrown  out  again  gradually  as  the 
speed  increases  and  the  back  E.M.F.  rises.*  Trolley  cars  are 
usually  run  by  two  motors  which,  on  starting,  work  in  series, 
so  that  each  supplies  a  part  of  the  starting  resistance  for  the 
other.  After  speed  is  acquired,  they  work  in  parallel. 

361.  The  recording  watt-hour  meter.  The  recording  watt- 
hour  meter  (Fig.  321)  is  the  instrument  which  fixes  our 
electric-light  bills.  It  is  essentially 
an  electric  motor  containing  no 
iron,  so  that  the  current  through 
the  armature  A  is  proportional  to 
the  P.D.  between  the  mains,  while 
the  current  through  the  field  mag- 
nets F  is  the  current  flowing  into 
the  house.  Therefore  the  force  act- 
ing between  A  and  F,  or  the  turning 
power  on  A  (torque),  is  propor- 
tional to  the  product  of  volts  by 
amperes ;  that  is,  it  is  proportional 

to  the  watts  consumed.  The  rate  of  rotation  is  made  slow  by 
the  magnetic  drag  due  to  the  reaction  between  the  magnets 
M  and  the  current  induced  in  the  rotating  aluminium  disk  D 
which  rotates  between  the  poles  of  the  magnets.  The  record- 
ing dials  have  therefore  a  speed  which  is  proportional  to  the 
'watts  used,  and  their  total  rotation  is  proportional  to  the  total 
energy,  or  watt  hours,  consumed. 

*  This  discussion  should  be  followed  by  a  laboratory  experiment  on  the 
study  of  a  small  electric  motor  or  dynamo.  See,  for  example,  Experiment 
No.  87  of  the  authors'  Manual. 


FIG.  321.  Interior  of  watt- 
hour  meter 


INDUCTION  COIL  AND  TBANSFOKMER         305 

QUESTIONS  AND  PROBLEMS 

1.  What  is  the  function  (use)  of  the  field  magnet  of  a  dynamo? 
Wood  is  cheaper  than  iron ;  why  are  not  the  field  cores  made  of  wood? 

2.  How  would  it  affect  the  voltage  of  a  dynamo  to  increase  the  speed 
of  rotation  of  its  armature  ?    Why  ?    to  increase  the  number  of  turns  of 
wire  in  the   armature  coils?   Why?    to  increase  the  strength  of  the 
magnetic  field?    Why? 

3.  When  a  wire  is  cutting  lines  of  force  at  the  rate  of  100,000,000 
per  second,  there  is  induced  in  it   an  E.M.F.  of  one  volt.    A  certain 
dynamo  armature  has  50  coils  of  5  loops  each  and  makes  600  revolutions 
per  minute.   Each  wire  cuts  2,000,000  lines  of  force  twice  in  a  revolution. 
What  is  the  E.M.F.  developed? 

4.  What  does  the  commutator  of  a  dynamo  do?    What  is  the  pur- 
pose of  the  commutator  of  a  motor  ? 

5.  Explain  the  process  of  "building  up  "  in  a  dynamo. 

6.  Explain  how  an  alternating  current  in  the  armature  is  trans- 
formed into  a  unidirectional  current  in  the  external  circuit. 

7.  Explain  why  a  series-wound  motor  can  run  on  either  a  direct  or 
an  alternating  circuit. 

8.  If  a  current  is  sent  into  the  armature  of  Fig.  313  at  V,  and  taken 
out  at  &,  which  way  will  the  armature  revolve  ? 

9.  Will  it  take  more  work  to  rotate  a  dynamo  armature  when  the 
circuit  is  closed  than  when  it  is  open  ?    Why  ? 

10.  Single  dynamos  often  operate  as  many  as  10,000  incandescent 
lamps  at  110  volts.   If  these  lamps  are  all  arranged  in  parallel  and  each 
requires  a  current  of  .5  ampere,  what  is  the  total  current  furnished  by 
the  dynamo  ?   What  is  the  activity  of  the  machine  in  kilowatts  and  in 
horse  power? 

11.  How  many  110-volt  lamps  like  those  of  Problem  10   can  be 
lighted  by  a  12,000-kilowatt  generator  ? 

12.  Why  does  it  take  twice  as  much  work  to  keep  a  dynamo  running 
when  1000  lights  are  on  t]ie  circuit  as  when  only  500  are  turned  on? 

PRINCIPLE  OF  THE  INDUCTION  COIL  AND  TRANSFORMER 
362.  Currents  induced  by  varying  the  strength  of  a  magnetic 

field.  Let  about  500  turns  of  No.  28  copper  wire  be  wound  around  one 
end  of  an  iron  core,  as  in  Fig.  322,  and  connected  to  the  circuit  of  a 
galvanometer  G.  Let  about  500  more  turns  be  wrapped  about  another 
portion  of  the  core  and  connected  into  the  circuit  of  two  dry  cells.  When 
the  key  K  is  closed,  the  deflection  of  the  galvanometer  will  indicate  that 


306  INDUCED  CUBKENTS 

a  temporary  current  has  been  induced  in  one  direction  through  the  coil 
s ;  and  when  it  is  opened,  an  equal  but  opposite  deflection  will  indicate 
an  equal  current  flow- 
ing in  the  opposite  x-^ — -,  »  p  ^ 

direction.  V^J ^  '  '""",      ,'ui\u»  _^ 

rrn  •  FIG.  322.    Induction  of  current  by  magnetizing 

experiment  and  demagnetizing  an  iron  core 

illustrates  the  prin- 
ciple of  the  induction  coil  and  the  transformer.  The  coil  jo, 
which  is  connected  to  the  source  of  the  current,  is  called  the 
primary  coil,  and  the  coil  s,  in  which  the  currents  are  induced, 
is  called  the  secondary  coil.  Causing  lines  of  force  to  spring 
into  existence  inside  of  s  (in  other  words,  magnetizing  the 
space  inside  of  s)  has  caused  an  induced  current  to  flow  in  s ; 
and  demagnetizing  the  space  inside  of  s  has  also  induced  a 
current  in  s  in  accordance  with  the  general  principle  stated  in 
§  348,  that  any  change  in  the  number  of  magnetic  lines  of  force 
which  thread  through  a  coil  induces  a  current  in  the  coil.  We 
may  think  of  the  lines  as  always  existing  as  closed  loops  (see 
Fig.  258,  p.  255)  which  collapse  upon  demagnetization  to 
mere  double  lines  at  the  axis  of  the  coil.  Upon  magnetization 
one  of  these  two  lines  springs  out,  cutting  the  encircling 
conductors  and  inducing  a  current. 

363.  Direction  of  the  induced  current.  Lenz's  law,  which, 
it  will  be  remembered,  followed  from  the  principle  of  conser- 
vation of  energy,  enables  us  to  predict  at  once  the  direction 
of  the  induced  currents  in  the  above  experiments ;  and  an 
observation  of  the  deflections  of  the  galvanometer  enables  us  to 
verify  the  correctness  of  the  predictions.  Consider  first  the  case 
in  which  the  primary  circuit  is  made  and  the  core  thus  magnet- 
ized. According  to  Lenz's  law  the  current  induced  in  the  sec- 
ondary circuit  must  be  in  such  a  direction  as  to  oppose  the  change 
which  is  being  produced  by  the  primary  current,  that  is,  in  such 
a  direction  as  to  tend  to  magnetize  the  core  oppositely  to  the 
direction  in  which  it  is  being  magnetized  by  the  primary.  This 


INDUCTION  COIL  AND  TRANSFORMER          307 

means,  of  course,  that  the  induced  current  in  the  secondary 
must  encircle  the  core  in  a  direction  opposite  to  the  direction 
in  which  the  primary  current  encircles  it.  We  learn,  therefore, 
that  on  making  the  current  in  the  primary  the  current  induced 
in  the  secondary  is  opposite  in  direction  to  that  in  the  primary. 
When  the  current  in  the  primary  is  broken,  the  magnetic 
field  created  by  the  primary  tends  to  die  out.  Hence,  by  Lenz's 
law,  the  current  induced  in  the  secondary  must  be  in  such  a 
direction  as  to  tend  to  oppose  this  process  of  demagnetization, 
that  is,  in  such  a  direction  as  to  magnetize  the  core  in  the  same 
direction  in  which  it  is  magnetized  by  the  decaying  current 
in  the  primary.  Therefore,  at  break  the  current  induced  in  the 
secondary  is  in  the  same  direction  as  that  in  the  primary. 

364.  E.M.F.  of  the  secondary.    If  half  of  the  500  turns  of 
the  secondary  s  (Fig.  322)  are  unwrapped,  the  deflection  will 
be  found  to  be  just  half  as  great  as  before.    Since  the  resistance 
of  the  circuit  has  not  been  changed,  we  learn  from  this  that 
the  E.M.F.  of  the  secondary  is  proportional  to  the  number  of 
turns  of  wire  upon  it, —  a  result  which  followed  also  from 
§  351.    If,  then,  we  wish  to  develop  a  very  high  E.M.F.  in 
the  secondary,  we  have  only  to  make  it  of  a  very  large  number 
of  turns  of  fine  wire. 

365.  Self-induction.     If,   in   the  experiment  illustrated  in 
Fig.  322,  the  coil  %  had  been  made  a  part  of  the  same  circuit  as 
p,  the  E.M.F.'s  induced  in  it  by  the  changes  in  the  magnetism 
of  the  core  would  of  course  have  been  just  the  same  as  above. 
In  other  words,  when  a  current  starts  in  a  coil,  the  magnetic 
field  which  it  itself  produces  tends  to  induce  a  current  oppo- 
site in  direction  to  that  of  the  starting  current,  that  is,  tends 
to  oppose  the  starting  of  the  current;   and  when  a  current 
in  a  coil  stops,  the  collapse  of  its  own  magnetic  field  tends  to 
induce  a  current  in  the  same  direction  as  that  of  the  stopping 
current,  that  is,  tends  to  oppose  the  stopping  of  the  current. 
This  means  merely  that  a  current  in  a  coil  acts  as  though  it  had 


308 


INDUCED  CURRENTS 


inertia,  and  opposes  any  attempt  to  start  or  stop  it.    This  inertia- 
like  effect  of  a  coil  upon  itself  is  called  self-induction. 

Let  a  few  dry  cells  be  inserted  into  a  circuit  containing  a  coil  of  a 
large  number  of  turns  of  wire,  the  circuit  being  closed  at  some  point  by 
touching  two  bare  copper  wires  together.  Holding  the  bare  wire  in  the 
fingers,  break  the  circuit  between  the  hands  and  observe  the  shock  due 
to  the  current  which  the  E.  M.  F.  of  self-induction  sends  through  your 
body.  Without  the  coil  in  circuit  you  will  obtain  no  such  shock, 
though  the  current  stopped  when  you  break  the  circuit  will  be  many 
times  larger. 

366.  The  induction  coil.  The  induction  coil,  as  usually 
made  (Fig.  323),  consists  of  a  soft  iron  core  C  composed  of 
a  bundle  of  soft  iron  wires  ;  a  primary  coil  p  wrapped  around 

this  core  and  consisting  of,  say, 
200  turns  of  coarse  copper  wire 


0) 


I      d 


(2) 


FIG.  323.   Induction  coil 

(for  example,  No.  16),  which  is  connected  into  the  circuit 
of  a  battery  through  the  contact  point  at  the  end  of  the  screw 
d\  a  secondary  coil  s  surrounding  the  primary  in  the  manner 
indicated  in  the  diagram  and  consisting  generally  of  between 
30,000  and  1,000,000  turns  of  No.  36  copper  wire,  the  termi- 
nals of  which  are  the  points  t  and  t' ;  and  a  hammer  b,  or 
other  automatic  arrangement  for  making  and  breaking  the 
circuit  of  the  primary.  (See  ignition  system  opposite  p.  199.) 

Let  the  hammer  b  be  held  away  from  the  opposite  contact  point  by 
means  of  the  finger,  then  touched  to  this  point,  then  pulled  quickly  away. 
A  spark  will  be  found  to  pass  between  t  and  i'  at  break  only  —  never  at  make. 
This  is  because,  on  account  of  the  opposing  influence  at  make  of  self- 
induction  in  the  primary,  the  magnetic  field  about  the  primary  rises 


INDUCTION  COIL  AND  TRANSFORMER 


309 


very  gradually  to  its  full  strength,  and  hence  its  lines  pass  into  the  sec- 
ondary coil  comparatively  slowly.  At  break,  however,  by  separating  the 
contact  points  very  quickly  we  can  make  the  current  in  the  primary  fall 
to  zero  in  an  exceedingly  short  time,  perhaps  not  more  than  .00001 
second ;  that  is,  we  can  make  all  of  its  lines  pass  out  of  the  coil  in  this 
time.  Hence  the  rate  at  which  lines  thread  through  or  cut  the  secondary 
is  perhaps  10,000  times  as  great  at  break  as  at  make,  and  therefore  the 
E.M.F.  is  also  something  like  10,000  times  as  great.  In  the  normal  use 
of  the  coil  the  circuit  of  the  primary  is  automatically  made  and  broken 
at  I  by  means  of  the  magnet  and  the  spring  r,  precisely  as  in  the  case  of 
the  electric  bell.  Let  the  student  analyze  this  part  of  the  coil  for  him- 
self. The  condenser  shown  in  the  diagram,  with  its  two  sets  of  plates 
connected  to  the  conductors  on  either  side  of  the  spark  gap  between  r 
and  d,  is  not  an  essential  part  of  a  coil,  but  when  it  is  introduced  it  is 
found  that  the  length  of  the  spark  which  can  be  sent  across  between  t 
and  t'  is  considerably  increased.  The  reason  is  as  follows :  When  the 
circuit  is  broken  at  b,  the  inertia  (that  is,  the  self-induction)  of  the 
primary  current  tends  to  make  a  spark  jump  across 
from  d  to  b ;  and  if  this  happens,  the  current  con- 
tinues to  flow  through  this  spark  (or  arc)  until  the 
terminals  have  become  separated  through  a  con- 
siderable distance.  This' makes  the  current  die 
down  gradually  instead  of  suddenly,  as  it  ought  to 
do  to  produce  a  high  E.M.F  ;  but  when  a  condenser 
is  inserted,  as  soon  as  b  begins  to  leave  d  the  current 
begins  to  flow  into  the  condenser,  and  this  gives  the 
hammer  time  to  get  so  far  away  from  d  that  an  arc  cannot  be  formed. 
This  means  a  sudden  break  and  a  high  E.  M.  F.  Since  a  spark  passes 
between  t  and  if  only  at  break,  it  must  always  pass 
in  the  same  direction.  Coils  which  give  24-inch 
sparks  (perhaps  500,000  volts)  are  not  uncommon. 
Such  coils  usually  have  hundreds  of  miles  of  wire 
upon  their  secondaries. 

367.  Laminated  cores ;  Foucault  currents.  The 
core  of  an  induction  coil  should  always  be  made  of 
a  bundle  of  soft-iron  wires  insulated  from  one  an- 
other by  means  of  shellac  or  varnish  (see  Fig.  324)  ; 
for  whenever  a  current  is  started  or  stopped  in  the 
primary  p  of  a  coil  furnished  with  a  solid  iron  core  (see  Fig.  325),  the 
change  in  the  magnetic  field  of  the  primary  induces  a  current  in  the 


FIG.  324.    Core  of 
insulated  iron  wire 


FIG.  325.  Diagram 
showing  eddy  cur- 
rents in  solid  core 


310 


INDUCED  CURRENTS 


FIG.  326.     Laminated    drum-armature 

core   with    commutator,   showing  one 

coil  wound  on  the  core 


conducting  core  C,  for  the  same  reason  that  it  induces  one  in  the  second- 
ary s.  This  current  flows  around  the  body  of  the  core  in  the  same 
direction  as  the  induced  current  in  the  secondary,  that  is,  in  the  direc- 
tion of  the  arrows.  The  only  effect  of  these  so-called  eddy  or  Foucault 
currents  is  to  heat  the  core.  This  is  obviously  a  waste  of  energy.  If 
we  can  prevent  the  appearance 
of  these  currents,  all  of  the  energy 
which  they  would  waste  in  heat- 
ing the  core  may  be  made  to 
appear  in  the  current  of  the 
secondary.  The  core  is  therefore 
built  of  varnished  iron  wires, 
which  run  parallel  to  the  axis  of 
the  coil,  that  is,  perpendicular  to 
the  direction  in  which  the  cur- 
rents would  be  induced.  The  induced  E.M.F.  therefore  finds  no  closed 
circuits  in  which  to  set  up  a  current  (Fig.  324).  It  is  for  the  same  rea- 
son that  the  iron  cores  of  dynamo  and  motor  armatures,  instead  of  being 
solid,  consist  of  iron  disks  placed  side  by  side,  as  shown  in  Fig.  326, 
and  insulated  from  one  another  by  films  of  oxide.  A  core  of  this  kind 
is  called  a  laminated  core.  It  will  be  seen  that  in  all  such  cores  the  spaces 
or  slots  between  the  laminae  must  run  at  right  angles  to  the  direction  of 
the  induced  E.M.F.,  that  is,  perpendicular  to  the  conductors  upon  the  core. 

368.  The  transformer.  The  commercial  transformer  is  a 
modified  form  of  the  induction  coil.  The  chief  difference  is 
that  the  core  R  (Fig.  327),  instead  of 
being  straight,  is  bent  into  the  form  of 
a  ring  or  is  given  some  other  shape  such 
that  the  magnetic  lines  of  force  have  a 
continuous  iron  path  instead  of  being 
obliged  to  push  out  into  the  air,  as  in 
the  induction  coil. 

always  an  alternating  instead  of  an  inter- 
mittent current  which  is  sent  through  the  primary  A.  Send- 
ing such  a  current  through  A  is  equivalent  to  first  magnetiz- 
ing the  core  in  one  direction,  then  demagnetizing  it,  then 
magnetizing  it  in  the  opposite  direction,  etc.  The  result  of 


TT<      ,  i  • ,     .       FIG.  327.    Diagram  of 

Furthermore,   it   .s  transform'er 


INDUCTION  COIL  AND  TRANSFORMER 


311 


Main  Conductor 


FlG'  m    Alternating-current  light- 
ing circuit  with  transformers 


these  changes  in  the  magnetism  of  the  core  is  of  course  an 
induced  alternating  current  in  the  secondary  B. 

369.  The  use  of  the  transformer.    The  use  of  the  transformer 
is  to  convert  an  alternating  current  from  one  voltage  to 
another  which,  for  some  rea- 

son,   is    found    to    be    more 

convenient.    For  example,  in 

electric  lighting  where  an  al- 

ternating current  is  used,  the 

E.M.F.   generated  by  the  dy- 

namo is  usually  either  1100 

or  2200  volts,  a  voltage  too 

high  to  be  introduced  safely 

into    private    houses.      Hence 

transformers    are    connected 

across  the  main  conductors  in  the  manner  shown  in  Fig.  328. 

The  current  which  passes  into  the  houses  to  supply  the  lamps 

does  not  come  directly  from  the  dynamo.    It  is  an  induced 

current  generated  in  the  transformer. 

Through  the  use  of  small  transformers  the  voltage  of  the 
current  of  the  house  lighting  circuit  is  further  reduced  and 
made  available  for  the  ringing  of  doorbells. 

370.  Pressure  in  primary  and  secondary.    If  there  are  a  few 
turns  in  the  primary  and  a  large  number  in  the  secondary,  the 
transformer  is  called  a  step-up  transformer,  because  the  P.D. 
produced  at  the  terminals  of  the  secondary  is  greater  than  that 
applied  at  the  terminals  of  the  primary.    In  electric  lighting, 
transformers  are  mostly  of  the  step-down  type  ;  that  is,  a  high 
P.D.  (say,  2200  volts)  is  applied  at  the  terminal  of  the  primary, 
and  a  lower  P.D.  (say,  110  volts)  is  obtained  at  the  terminals 
of  the  secondary.    In  such  a  transformer  the  primary  will  have 
twenty  times  as  many  turns  as  the  secondary.    In  general,  the 
ratio  between  the  voltages  at  the  terminals  of  the  primary  and 
secondary  is  the  ratio  of  the  number  of  turns  of  wire  upon  the  two. 


312 


INDUCED  CURRENTS 


371.  Efficiency  of  the  transformer.    In  a  perfect  transformer 
the  efficiency  would  be  unity.    This  means  that  the  electrical 
power,  or  watts,  put  into  the  primary  (that  is,  the  volts  applied 
to  its  terminals  times  the  amperes  flowing  through  it)  would  be 
exactly  equal  to  the  power,  or  watts,  taken  out  in  the  secondary 
(that  is,  the  volts  generated  in  it  times  the  strength  of  the  in- 
duced current)  ;  and,  in  fact,  in  actual  transformers  the  latter 
product  is  often  more  than  97%  of  the  former  (that  is,  there 
is  less  than  3%  loss  of  energy  in  the  transformation).  This  lost 
energy  appears  as  heat  in  the  transformer.  This  transfer,  which 
goes  on  in  a  big  transformer,  of  huge  quantities  of  power 
from  one  circuit  to  another  entirely  independent  circuit,  with- 
out noise  or  motion  of  any  sort  and  almost  without  loss,  is  one 
of  the  most  wonderful  phenomena  of  modern  industrial  life. 

372.  Commercial  transformers.   Fig.  329  illustrates  a  common  type  of 
transformer  used  in  electric  lighting.    The  core  is  built  up  of  sheet-iron 
laminae  about  ^  millimeter  thick.    Fig.  330  shows  a  section  of  the  same 


FIG.  329.   The  core  type 
of  transformer 


FIG.  330.  Cross  sec- 
tion of  transformer, 
showing    shape    of 
magnetic  field 


FIG.  331.   Trans- 
former case 


transformer.  The  closed  magnetic  circuit  of  the  core  is  indicated  by  the 
dotted  lines.  The  primaries  and  the  secondaries  are  indicated  by  the 
letters  P  and  S.  Fig.  331  is  the  case  in  which  the  transformer  is  placed. 
Such  cases  may  be  seen, attached  to  poles  outside  of  houses  wherever 
alternating  currents  are  used  for  electric  lighting  (Fig.  332). 

373.  Electrical  transmission  of  power.  Since  the  rate  of  production 
of  electrical  energy  by  a  dynamo  is  the  product  of  the  E.M.F.  generated 
by  the  current  furnished,  it  is  evident  that  in  order  to  transmit  from 


INDUCTION  COIL  AND  TRANSFORMER         313 


Transformer 


one  point  to  another  a  given  number  of  watts,  say,  10,000,  it  is  pos- 
sible to  have  either  an  E.M.F.  of  100  volts  and  a  current  of  100  amperes 
or  an  E.M.F.  of  1000  volts  and  a  current  of  10  amperes.  In  the  two 
cases,  however,  the  loss  of  energy  in 
the  wire  which  carries  the  current 
from  the  place  where  it  is  generated 
to  the  place  where  it  is  used  will  be 
widely  different.  For, 

watts  —  amperes  x  volts ; 
but,  from  Ohm's  law, 

volts  =  amperes  x  ohms. 
Therefore 

watts  =  amperes2  x  ohms  =  I2R. 

If,  then,  R  represents  the  resistance 
of  this  transmitting  wire,  the  so- 
called  "line  resistance,"  and  /  the 
current  flowing  through  it,  the  heat 
developed  in  it  will  be  proportional 
to  I'2R.  Hence  the  energy  wasted 
in  heating  the  line  will  be  but  ^-^ 
as  much  in  the  case  of  the  1000  volt, 

10-ampere  current  as  in  the  case  of  the  100  volt,  100-ampere  current. 
Hence  for  long-distance  transmission,  where  line  losses  are  considerable, 
it  is  important  to  use  the  highest  possible  voltages. 

On  account  of  the  difficulty  of  insulating  the  commutator  segments 
from  one  another,  voltages  higher  than  1200  or  1500  cannot  be  obtained 
with  direct-current  dynamos  of  the  kind  that  have  been  described. 
With  alternators,  however,  the  difficulties  of  insulation  are  very  much 
less  on  account  of  the  absence  .of  a  commutator.  The  large  10,000- 
horse-power  alternating-current  dynamos  on  the  Canadian  side  of 
Niagara  Falls  generate  directly  12,000  volts.  This  is  the  highest  volt- 
age thus  far  produced  by  generators.  In  all  cases  where  these  high 
pressures  are  employed  they  are  transformed  down  at  the  receiving  end 
of  the  line  to  a  safe  and  convenient  voltage  (from  50  to  500  volts)  by 
means  of  step-down  transformers. 

It  will  be  seen  from  the  above  facts  that  alternating  currents  are 
best  suited  for  long-distance  transmission.  The  Big  Creek  plant  in 
California  transmits  power  241  miles  at  a  pressure  of  150,000  volts. 
(See  opposite  p.  241.)  The  Southern  Sierras  Power  Company  of 


FIG.  332.    Transformer  on  electric- 
light  pole 


814 


INDUCED  CURRENTS 


California  sends  current  830  miles  across  the  desert.  Transmission  at 
220,000  volts  is  now  under  consideration  for  a  line  to  extend  the  length 
of  California,  over  1100  miles.  In  all  such  cases  step-up  transformers, 
situated  at  the  power  house,  transfer  the  electrical  energy  developed  by 


2.200  volts 


22.000  volts 


22,000 


2,200 


Alternator 


m 
Transformer 


Step-down          wv( 
Transformer     [\uol        \o\uo 


Motcr      Lamps 


Power  House  Distant  City 

FIG.  333.    High- voltage  long-distance  transmission  line 


the  generator  to  the  line,  and  step-down  transformers,  situated  at  the 
receiving  end,  transfer  it  to  the  motors  or  lamps  which  are  to  be  sup- 
plied (Fig.  333).  The  generators  used  on  the  American  side  of  Niagara 
Falls  produce  a  pressure  of  2300  volts.  For  transmis- 
sion to  Buffalo,  20  miles  away,  this  is  transformed  up 
to  22,000  volts.  At  Buffalo  it  is  transformed  down  to 
the  voltages  suitable  for  operating  the  street  cars, 
lights,  and  factories  of  the  city.  On  the  Canadian  side 
the  generators  produce  currents  at  12,000  volts,  as 
stated,  and  these  are  transformed  up,  for  long-distance 
transmission,  to  22,000,  40,000,  and  60,000  volts  (see 
Fig.  166,  p.  150). 

374.  The  tungar  rectifier.  Negative  electrons  are 
found  to  escape  from  a  filament  that  is  heated  to  in- 
candescence, and  if  this  filament  is  then  made  more 
than,  say,  25  volts  negative  with  respect  to  a  near-by 
anode  any  gas  that  surrounds  the  filament  is  found  to 
be  ionized  (split  into  positively  and  negatively  charged 
parts)  by  the  violence  of  the  blows  which  the  electrons 
strike  against  its  molecules.  It  is  thus  rendered  con- 
ducting. These  facts  are  utilized  in  the  tungar  rectifier 
of  the  alternating  current.  The  bulb  (Fig.  334)  is  filled  with  argon  to  a 
pressure  of  3  to  8  cm.  The  anode  is  a  small  cone  of  graphite  or  tungsten, 


FIG.  334.    Tun- 
gar bulb 


INDUCTION  COIL  AND  TRANSFORMER         315 


FIG.  335.    Principle  of  opera- 
tion of  the  tungar  rectifier 


and  the  cathode  is  a  coiled  tungsten  filament.  When  the  rectifier 
is  in  operation,  the  cone  and  the  filament  are  alternately  +  and  — ,  one 
being  +  while  the  other  is  — .  When  the  cone  is  -f  and  the  filament  — , 
the  negative  electrons  from  the  filament 
are  forced  across  the  space  from  the  fila- 
ment to  the  cone,  and  the  argon,  which 
is  thereby  ionized,  carries  the  current 
from  the  cone  to  the  filament.  When  the 
cone  is  —  and  the  filament  +,  the  nega- 
tive electrons  cannot  escape  from  the 
filament ;  hence  the  gas  does  not  become 
conducting.  The  principle  of  operation 
can  be  understood  from  Fig.  335. 

The  rectifier  is  connected  to  the  alternating-current  line  at  C  and  D. 
The  alternating  current  in  the  primary  coil  P  of  the  transformer  T 
causes  an  induced  current  in  S,  which  keeps  the  filament  F  incandes- 
cent. Under  the  action  of  the  current,  A  and  F  are  alternately  +  and  — . 
When  ,P  is  — ,  the  electrons  escape  and  ionize  -the  gas,  permitting  the 
current  to  pass.  When  .F  is  +  the  negative  electrons  are  driven  back 
into  the  filament  and  cannot  escape  to  ionize  the  gas.  Hence  no  current 
passes.  In  this  way  a  unidirectional  pulsating  current  passes  through 
the  storage  batteries  or  other  load.  This  rectifier  is  used  largely  for 
charging  storage  batteries  for  small-power  purposes. 

375.  Principle  of  the  carbon  microphone.  Let  a  dry  cell,  an 
ammeter,  and  two  pieces 'of  electric-arc  carbon  be  arranged  in  series 
(Fig.  336).  Press  the  carbons  very  gently  and 
observe  the  reading  of  the.  ammeter.  Press 
,  gradually  harder,  then  gradually  less,  watch- 
ing the  instrument.  The  current  increases 
with  increase  in  pressure,  and  decreases  with 
decrease  in  pressure. 


FIG.  336.    The  principle 
of  the  carbon  transmitter 


This  peculiar  behavior  of  carbon  in 
offering  a  variable  resistance  with  varia- 
tion in  pressure  is  taken  advantage  of  in  constructing  the 
carbon  transmitter  of  the  telephone.  In  the  modern  trans- 
mitter, however,  the  current  is  made  to  traverse  many  particles 
of  granular  carbon,  which,  lying  loosely  together,  furnish  a 
very  great  number  of  loose  contacts  (see  Fig.  339). 


316  INDUCED  CURRENTS 

376.  Principle  of  the  telephone.  The  telephone  was  invented 
in  1875  by  Alexander  Graham  Bell  of  Washington  (see  on 
opposite  page)  and  Elisha  Gray  of  Chicago.  The  simple 
local-battery  system  is  shown  in  Fig.  337. 

The  current  from  the  battery  B  (Fig.  337)  is  led  first  to 
the  back  of  the  diaphragm  E,  whence  it  passes  through  a  little 
chamber  C,  filled  with  granular  carbon,  to  the  conducting 
back  d  of  the  transmitter,  and  thence  through  the  primary  p 
of  the  induction  coil,  and  back  to  the  battery. 

When  a  sound  is  made  in  front  of  the  microphone,  the 
vibrations  produced  by  the  sounding  body  are  transmitted  by 

Receiver  Receiver 


B  B 

FIG.  337.   The  telephone  circuit  (local-battery  system) 

the  air  to  the  diaphragm,  thus  causing  the  latter  to  vibrate 
back  and  forth.  These  vibrations  of  the  diaphragm  vary  the 
pressure  upon  the  many  contact  points  of  the  granular  carbon 
through  which  the  primary  current  flows.  This  produces  con- 
siderable variation  in  the  resistance  of  the  primary  circuit,  so 
that  as  the  diaphragm  moves  forward,  that  is,  toward  the  carbon, 
a  comparatively  large  current  flows  through  p,  and  as  it  moves 
back  a  much  smaller  current.  These  changes  in  the  current 
strength  in  the  primary  p  produce  changes  in  the  magnetism 
of  the  soft-iron  core  of  the  induction  coil.  Currents  are 
therefore  induced  in  the  secondary  s  of  the  induction  coil,  and 
these  currents  pass  over  the  line  and  affect  the  receiver  at 
the  other  end.  A  step-up  induction  coil  is  used  to  get 
sufficient  potential  to  work  through  the  high  resistance  of  a 
long  line. 


©  Clinedinet 

ALEXANDER  GRAHAM  BELL, 

WASHINGTON,  D.C. 
Inventor  of  the  telephone,  1875 


©  Underwood  &  Underwood 

THOMAS  A.  EDISON,  ORANGE, 
NEW  JERSEY 

Inventor  of  the  phonograph,  the  incan- 
descent lamp,  etc. 


GUGLIELMO  MARCONI  (ITALY)  ORVILLE  WRIGHT,  DAYTON,  OHIO 

Inventor  of  commercial  wireless  Inventor,  with  his  brother  Wilbur,  of 

telegraphy  the  airplane 

A  GROUP  OF  MODERN  INVENTORS 


THE  WRIGHT  AIRPLANE 

The  most  significant  and  far-reaching  of  the  advances  of  the  twentieth  century, 
namely,  man's  conquest  of  the  air  after  centuries  of  failure,  was  made  when  the 
Wright  brothers  first  introduced  the  principle  upon  which  all  successful  flight  by 
heavier-than-air  machines  now  depends,  namely,  control  of  stability  by  the  warp- 
ing of  wings,  or  by  ailerons  (hinged  attachments  to  wings),  in  connection  with  the 
use  of  a  rudder.  The  ripper  panel  shows  one  of  the  original  gliders  (Wilbur 
Wright  inside)  with  which  the  Wrights  first  mastered  the  art  of  gliding  (1900- 
1903)  and  made  more  than  a  thousand  gliding  flights,  some  of  them  GOO  feet  long, 
following  in  this  work  the  principles  of  gliding  flight  first  demonstrated  by 
Lilienthal  and  a  little  later,  much  more  completely,  by  Chanute  of  Chicago  (1895- 
1897) .  The  lower  panel  shows  "  the  first  successful  power  flight  in  the  history  of  the 
world  "  (Orville  Wright  in  the  machine,  Wilbur  running  beside  it  as  it  rose  from 
the  track) .  Four  such  flights  were  made  on  the  morning  of  December  17,  1903, 
the  longest  of  which  lasted  59  seconds  and  covered  a  distance  of  852  feet  against 

a  20-mile  wind 


INDUCTION  COIL  AND  TRANSFORMER 


317 


FIG.  338.    The  modern  receiver 


A  modern  telephone  receiver  is  shown  in  Fig.  338.  It 
consists  of  a  permanently  magnetized  U-shaped  piece  of  steel 
in  front  of  whose 
poles  is  a  soft-iron 
diaphragm  which 
almost  touches  the 
ends  of  the  mag- 
net. Wound  in 
opposite  directions 
upon  the  two  poles 
are  coils  of  fine 
insulated  wire  in 
series  with  each  other  and  the  line  wire.  G-  is  the  earpiece, 
E  the  diaphragm,  A  the  U-shaped  magnet,  and  B  the  coils, 
consisting  of  many  turns  of  fine  wire  and  having  soft-iron 
cores.  When  the  rapidly  alternating  current  from  the  secondary 
coil  s  (Fig.  337)  flows  through  the  coils  of  the  receiver, the  poles 
of  the  permanent  magnet  are  thereby  alternately  strengthened 
and  weakened  in  synchronism  with  the  sound  waves  falling 
upon  the  diaphragm  of  the  transmitter.  The  variations  in 
the  magnetic  pull  upon  the  diaphragm 
of  the  receiver  cause  it  to  send  out 
sound  waves  exactly  like  those  which 
fell  upon  the  diaphragm  of  the  trans- 
mitter. 

Telephonic  conversation  can  be  car- 
ried on  over  great  distances  as  rapidly 
as  if  the  parties  sat  on  opposite  sides 
of  the  same  table.  An  electrical  im- 
pulse passes  over  the  telephone  wires 
from  New  York  to  San  Francisco  in 

about  one  fifteenth  of  a  second.  The  cross  section  of  a  complete 
long-distance  transmitter  is  shown  in  Fig.  339.  The  current 
traverses  granular  carbon  held  between  solid  blocks  of  carbon. 


FIG  .  339.  Cross  section  of 

a  long-distance  telephone 

transmitter 


318  INDUCED  CUKKENTS 

QUESTIONS  AND  PROBLEMS 

1.  Draw  a  diagram  of  an  induction  coil  and  explain  its  action. 

2.  Does  the  spark  of  an  induction  coil  occur  at  make  or  at  break  ? 
Why? 

3.  Explain  why  an  induction  coil  is  able  to  produce  such  an  enor- 
mous E.M.F. 

4.  Why  could  not  an  armature  core  be  made  of  coaxial  cylinders  of 
iron  running  the  full  length  of  the  armature,  instead  of  flat  disks,  as 
shown  in  Fig.  326  ? 

5.  What  relation  must  exist  between  the  number  of  turns  on  the 
primary  and  secondary  of  a  transformer  which  feeds  110-volt  lamps 
from  a  main  line  whose  conductors  are  at  1100  volts  P.D.? 

6.  Name  two  uses  and  two  disadvantages  of  mechanical  friction ;  of 
electrical  resistance. 

7.  A  transformer  is  so  wound  as  to  step  the  voltage  of  the  lighting 
circuit  from  2200  volts  down  to  110.    Sketch  the  transformer  and  its 
connections,  marking  the  primary  and  the  secondary,  and  state  the 
relative  number  of  turns  in  each.    If  the  house  circuit  uses  40  amperes, 
what  current  must  flow  in  the  primary  ? 

8.  Why  does  a  " tungar "  rectify  an  alternating  current? 

9.  The  same  amount  of  power  is  to  be  transmitted  over  two  lines 
from  a  power  plant  to  a  distant  city.  If  the  heat  losses  in  the  two  lines 
are  to  be  the  same,  what  must  be  the  ratio  of  the  cross  sections  of  the 
two  lines  if  one  current  is  transmitted  at  100  volts  and  the  other  at 
10,000  volts?   (Power  =  IE;  heat  loss  is  proportional  to  7272.) 

10.  In  telephoning  from  New   York  to  San  Francisco  how  far  do 
you  think  the  sound  goes  ?   What  passes  along  the  telephone  wire  ? 


CHAPTER  XVI* 

NATURE  AND  TRANSMISSION  OF  SOUND 
SPEED  AND  NATURE  OF  SOUND 

377.  Sources  of  sound.    If  a  sounding  tuning  fork  provided 
with  a  stylus  is  stroked  across  a  smoked-glass  plate,  it  produces 
a  wavy  line,  as  shown  in  Fig.  340 ;  if  a  light  suspended  ball 
is  brought  into  contact  with  it,  the  latter  is  thrown  off  with 
considerable  violence.     If    we  look 

about  for  the  source  of  any  sudden     ^^^r ' Wr^S*~~~- 

«/  »' inpitm^Q—*-*' 

noise,  we  find  that  some  object  has      FJG  m   Trace  ma<Je  by 
fallen,  or  some  collision  has  occurred,  vibrating  fork 

or  some  explosion  has  taken  place, 

—  in  a  word,  that  some  violent  motion  of  matter  has  been  set 
up  in  some  way.  From  these  familiar  facts  we  conclude  that 
sound  arises  from  the  motions  of  matter. 

378.  Media  of  transmission.    Air  is  ordinarily  the  medium 
through  which  sound  comes  to  our  ears,  yet  the  Indians  put 
their  ears  to  the  ground  to  hear  a  distant  noise,  and  most  boys 
know  how  loud  the  clapping  .of  stones  sounds  under  water. 
If  the  base  of  the  sounding  fork  of  Fig.  340  is  held  in  a  dish 
of  water,  the  sound  will  be  markedly  transmitted  by  the  water. 
These  facts  show  that  a  gas  like  air  is  certainly  no  more 
effective  in   the  transmission   of   sound  than  a   liquid  or  a 
solid.    Next  let  us  see  whether  or  not  matter  is  necessary 
at  all  for  the  transmission  of  sound. 

*  This  chapter  should  be  accompanied  by  laboratory  experiments  on  the 
speed  of  sound  in  air,  the  vibration  rate  of  a  fork,  and  the  determination 
of  wave  lengths.  See,  for  example,  Experiments  38, 39,  and  40  of  the  authors' 
Manual. 

319 


320      NATUKE  AND  TRANSMISSION  OF  SOUND 

Let  an  electric  bell  be  suspended  inside  the  receiver  of  an  air  pump 
by  means  of.  two  fine  springs  which  pass  through  a  rubber  stopper  in 
the  manner  shown  in  Fig.  341.  Let  the  air  be  exhausted  from  the 
receiver  by  means  of  the  pump.  The  sound  of  the 
bell  will  be  found  to  become  less  and  less  pro- 
nounced. Let  the  air  be  suddenly  readmitted. 
The  volume  of  sound  will  at  once  increase. 

Since  the  nearer  we  approach  a  vacuum, 
the  less  distinct  becomes  the  sound,  we  infer 
that  sound  cannot  be  transferred  through 
a  vacuum  and  that  therefore  the  transmis- 
sion of  sound  is  effected  only  through  the  FlG-341.  Sound  not 
/.  7  •  T  , ,  .  transmitted  through 

agency  oj  ordinary  matter.    In  this  respect 

sound  differs  from  heat  and  light,  which 

evidently   pass  with   perfect  readiness    through   a   vacuum, 

since  they  reach  the  earth  from  the  sun  and  stars. 

379.  Speed  of  transmission.  The  first  attempt  to  measure 
accurately  the  speed  of  sound  was  made  in  1738,  when  a  com- 
mission of  the  French  Academy  of  Sciences  stationed  two 
parties  about  three  miles  apart  and  observed  the  interval 
between  the  flash  of  a  cannon  and  the  sound  of  the  report. 
By  taking  observations  between  the  two  stations,  first  in  one 
direction  and  then  in  the  other,  the  effect  of  the  wind  was 
eliminated.  A  second  commission  repeated  these  experiments 
in  1832,  using  a  distance  of  18.6  kilometers,  or  a  little  more 
than  11.5  miles.  The  value  found  was  331. 2.  meters  per  sec- 
ond at  0°  C.  The  accepted  value  is  now  331.3  meters.  The 
speed  in  water  is  about  1400  meters  per  second,  and  in  iron 
5100  meters. 

The  speed  of  sound  in  air  is  found  to  increase  with  an  in- 
crease in  temperature.  The  amount  of  this  increase  is  about 
60  centimeters  per  degree  centigrade.  Hence  the  speed  at 
20°  C.  is  about  343.3  meters  per  second.  The  above  figures 
are  equivalent  to  1087  feet  per  second  at  0°C.,  or  1126  feet 
per  second  at  20°  C. 


SPEED  AND  NATURE  OF  SOUND  321 

380.  Mechanism  of  transmission.  When  a  firecracker  or  toy 
cap  explodes,  the  powder  is  suddenly  changed  to  a  gas,  the 
volume  of  which  is  enormously  greater  than  the  volume  of 
the  powder.  The  air  is  therefore  suddenly  pushed  back  in  all 
directions  from  the  center  of  the  explosion.  This  means  that 
the  air  particles  which  lie  about  this  center  are  given  violent 
outward  velocities.*  When  these  outwardly  impelled  air  parti- 
cles collide  with  other  particles,  they  give  up  their  outward 
motion  to  these  second  particles,  and  these  in  turn  pass  it  on 
to  others,  etc.  It  is  clear,  therefore,  that  the  motion  started  by 
the  explosion  must  travel  on  from  particle  to  particle  to  an 
indefinite  distance  from  the  center  of  the  explosion.  Further- 
more, it  is  also  clear  that,  although  the  motion  travels  on  to 
great  distances,  the  individual  particles  do  not  move  far  from 
their  original  positions;  for  it  is  easy 
to  show  experimentally  that  whenever 
an  elastic  body  in  motion  collides  with 
another  similar  body  at  rest,  the  collid- 
ing body  simply  transfers  its  motion  to 

the  body  at  rest  and  comes  itself  to  rest. 

FIG.  342.    Illustrating  the 

Let  six  or  eight  equal  steel  balls  be  hung  propagation  of  sound  from 
from  cords  in  the  manner  shown  in  Fig.  342.  particle  to  particle 

First  let  all  of  the  balls  but  two  adjacent 

ones  be  held  to  one  side,  and  let  one  of  these  two  be  raised  and  allowed 
to  fall  against  the  other.  The  first  ball  will  be  found  to  lose  its  motion 
in  the  collision,  and  the  second  will  be  found  to  rise  to  practically  the 
same  height  as  that  from  which  the  first  fell.  Next  let  all  of  the  balls  be 
placed  in  line  and  the  end  one  raised  and  allowed  to  fall  as  before.  The 
motion  will  be  transmitted  from  ball  to  ball,  each  giving  up  the  whole 
of  its  motion  practically  as  soon  as  it  receives  it,  and  the  last  ball  will 
move  on  alone  with  the  velocity  which  the  first  ball  originally  had. 

*  These  outward  velocities  are  simply  superposed  upon  the  velocities  of 
agitation  which  the  molecules  already  have  on  account  of  their  temperature. 
For  our  present  purpose  we  may  ignore  entirely  the  existence  of  these  latter 
velocities  and  treat  the  particles  as  though  they  were  at  rest,  save  for  the 
velocities  imparted  by  the  explosion. 


322      NATURE  AND  TRANSMISSION  OF  SOUND 

The  preceding  experiment  furnishes  a  very  nice  mechanical 
illustration  of  the  manner  in  which  the  air  particles  which 
receive  motions  from  an  exploding  firecracker  or  a  vibrating 
tuning  fork  transmit  these  motions  in  all  directions  to  neigh- 
boring layers  of  air,  these  in  turn  to  the  next  adjoining  layers, 
etc.,  until  the  motion  has  traveled  to  very  great  distances, 
although  the  individual  particles  themselves  move  only  very 
minute  distances.  When  a  motion  of  this  sort,  transmitted 
by  air  particles,  reaches  the  drum  of  the  ear,  it  produces  the 
sensation  which  we  call  sound. 

381.  A  train  of  waves  ;  wave  length.  In  the  preceding  para- 
graphs we  have  confined  attention  to  a  single  pulse  traveling 
out  from  a  center  of  explosion.   Let  us  next  consider  the  sort 
of  disturbance  which  is  set     ABC 
up  in  the  air  by  a  con  tin-      \  /          J 
uously  vibrating  body,  like        \\  VcTe'i — th 

the  prong  of  Fig.  343.    Each       m 

time  that  this  prong  moves 

.,         .    ,  ,    ..  -,  FIG.  343.  Vibrating  reed  sending  out  a 

to  ihe  right  it  sends  out  a  train  of  cq^sstant  pulses 

pulse  which  travels  through 

the  air  at  the  rate  of  1100  feet  per  second,  in  exactly  the 
manner  described  in  the  preceding  paragraphs.  Hence,  if  the 
prong  is  vibrating  uniformly,  we  shall  have  a  continuous 
succession  of  pulses  following  each  other  through  the  air  at 
exactly  equal  intervals.  Suppose,  for  example,  that  the  prong 
makes  110  complete  vibrations  per  second.  Then  at  the  end 
of  one  second  the  first  pulse  sent  out  will  have  reached  a 
distance  of  1100  feet.  Between  this  point  and  the  prong 
there  will  be  110  pulses  distributed  at  equal  intervals;  that 
is,  each  two  adjacent  pulses  will  be  just  10  feet  apart.  If 
the  prong  made  220  vibrations  per  second,  the  distance  be- 
tween adjacent  pulses  Avould  be  5  feet,  etc.  The  distance, 
letiveen  two  adjacent  pulses  in  such  a  train  of  waves  is  called 
a  wave  length. 


SPEED  AND  NATURE  OF  SOUND  323 

382.  Relation  between  velocity,  wave  length,  and  number 
of  vibrations  per  second.    If  n  represents  the  number  of  vibra- 
tions per  second  of  a  source  of  sound,  I  the  wave  length,  and  v 
the  velocity  with  which  the  sound  travels  through  the  medium, 
it  is  evident  from  the  example  of  the  preceding  paragraph  that 
the  following  relation  exists  between  these  three  quantities : 

I  =  v/n,  or  v  =  nl ;  (1) 

that  is,  wave  length  is  equal  to  velocity  divided  by  the  number  of 
vibrations  per  second,  or  velocity  is  equal  to  the  number  of  vibra- 
tions per  second  times  the  wave  length. 

383.  Condensations  and  rarefactions.   Thus  far,  for  the  sake 
of  simplicity,  we  have  considered  a  train  of  waves  as  a  series 
of  thin,  detached  pulses  separated  by  equal  intervals  of  air  at 
rest.    In  point  of  fact,  however,  the  air  in  front  of  the  prong 
B  (Fig.  343)  is  being  pushed  forward  not  at  one  particular 

ABC 


FIG.  344.  Illustrating  motions  of  air  particles  in  one  complete  sound  wave 
consisting  of  a  condensation  and  a  rarefaction 

instant  only  but  during  all  the  time  that  the  prong  is  moving 
from  A  to  (7,  that  is,  through  the  time  of  one-half  vibration  of 
the  fork  ;  and  during  all  this  time  this  forward  motion  is  being 
transmitted  to  layers  of  air  which  are  farther  and  farther  away 
from  the  prong,  so  that  when  the  latter  reaches  (7,  all  the  air 
between  C  and  some  point  c  (Fig.  344)  one-half  wave  length 
away  is  crowding  forward  and  is  therefore  in  a  state  of  com- 
pression, or  condensation.  Again,  as  the  prong  moves  back  from 
C  to  A,  since  it  tends  to  leave  a  vacuum  behind  it,  the  adja- 
cent layer  of  air  rushes  in  to  fill  up  this  space,  the  layer  next 
adjoining  follows,  etc.,  so  that  when  the  prong  reaches  A,  all 
the  air  between  A  and  c  (Fig.  344)  is  moving  backward  and 

\ 


324      NATURE  AND  TRANSMISSION  OF  SOUND 


is  therefore  in  a  state  of  diminished  density,  or  rarefaction. 

During  this  time  the  preceding  forward  motion  has  advanced 

one  half  wave  length  to  the  right,  so  that  it  now  occupies  the 

region  between  c  and  a  (Fig.  344).  Hence  at  the  end  of  one 

complete  vibration  of  the  prong  we  may  divide  the  air  between 

it  and  a  point  one  wave 

length  away  into  two 

portions,  one  a  region 

of  condensation  ac,  and 

the  other  a  region  of 

rarefaction  ca.  The  ar-         "bcdefghij 

rows  in  Fig.  344  rep- 

resent  the  direction  and  relative  magnitudes  of  the  motions 

of  the  air  particles  in  various  portions  of  a  complete  wave. 

At  the  end  of  n  vibrations  the  first  disturbance  will  have 
reached  a  distance  n  wave  lengths  from  the  fork,  and  each  wave 
between  this  point  and  the  fork  will  consist  of  a  condensation 
and  a  rarefaction,  so  that  sound  waves  may  be  said  to  consist 
of  a  series  of  condensations  and  rarefactions  following  one 
another  through  the  air  in  the  manner  shown  in  Fig.  345. 

Wave  length  may  now  be  more  accurately  defined  as  the 
distance  between  two  successive  points  of  maximum  condensation 
(b  and  /,  Fig.  345)  or  of  maximum  rarefaction  (d  and  h). 

384.  Water-wave  analogy.  Condensations  and  rarefactions 
of  sound  waves  are  exactly  analogous  to  the  familiar  crests  and 
troughs  of  water  waves.  #  /  j 

Thus,  the  wave  length  of 
such  a  series  of  waves  as 
that  shown  in  Fig.  346  is 
defined  as  the  distance  bf 
between  two  crests,  or  the  distance  dh,  or  ae,  or  eg,  or  mn, 
between  any  two  points  which  are  in  the  same  condition,  or  phase, 
of  disturbance.  The  crests  (that  is,  the  shaded  portions,  which 
are  above  the  natural  level  of  the  water)  correspond  exactly 


d  h 

FIG.  346.    Illustrating  wave  length  of 
water  waves 


SPEED  AND  NATURE  OF  SOUND 


325 


to  the  condensations  of  sound  waves  (that  is,  to  the  portions  of 
air  which  are  above  the  natural  density).  The  troughs  (that  is, 
the  dotted  portions)  correspond  to  the  rarefactions  of  sound 
waves  (that  is,  to  the  portions  of  air  which  are  below  the  nat- 
ural density).  But  the  analogy  breaks  down  at  one  point,  for 
in  water  waves  the  motion  of  the  particles  is  transverse  to  the 
direction  of  propagation,  while  in  sound  waves,  as  shown  in 
§  383,  the  particles  move  back  and  forth  in  the  line  of  propaga- 
tion of  the  wave.  Water  waves  are  therefore  called  transverse 
waves,  while  sound  waves  in  air  are  called  longitudinal  waves. 

385.  Distinction  between  musical  sounds  and  noises.    Let  a 

current  of  air  from  a  -|-inch  nozzle  be  directed  against  a  row  of 
forty-eight  equidistant  i-inch  holes  in  a  metal 
or  cardboard  disk,  mounted  as  in  Fig.  347  and 
set  into  rotation  either  by  hand  or  by  an  elec- 
tric motor.  A  very  distinct  musical  tone  will 
be  produced.  Then  let  the  jet  of  air  be  directed 
against  a  second  row  of  forty-eight  holes,  which 
differs  from  the  first  only  in  that  the  holes  are 
irregularly  instead  of  regularly  spaced  about 
the  circumference  of  the  disk.  The  musical 
character  of  the  tone  will  altogether  disappear. 

The  experiment  furnishes  a  very 
striking  illustration  of  the  difference  be- 
tween a  musical  sound  and  a  noise. 
Only  those  sounds  possess  a  musical  qual- 
ity which  come  from  sources  capable  of 
sending  out  pulses,  or  waves,  at  absolutely 

regular  intervals.  Therefore  it  is  only  sounds  possessing  a 
musical  quality  which  may  be  said  to  have  wave  lengths. 

386.  Pitch.    While  the  apparatus  of  the  preceding  experiment  is 
rotating  at  constant  speed,  let  a  current  of  air  be  directed  first  against 
the  outside  row  of  regularly  spaced  holes  and  then  suddenly  turned 
against  the  inside  row,  which  is  also  regularly  spaced  but  which  contains 
a  smaller  number  of  holes.    The  note  produced  in  the  second  case  will 


FIG.  347.    Regularity  of 

pulses  the  condition  for 

a  musical  tone 


326      NATURE  AND  TRANSMISSION  OF  SOUND 

be  found  to  have  a  markedly  lower  pitch  than  the  other  one.  Again 
let  the  jet  of  air  be  directed  against  one  particular  row,  and  let  the  speed 
of  rotation  be  changed  from  very  slow  to  very  fast.  The  note  produced 
will  gradually  rise  in  pitch. 

We  conclude,  therefore,  that  the  pitch  of  a  musical  note  de- 
pends simply  upon  the  number  of  pulses  which  strike  the  ear  per 
second.  If  the  sound  comes  from  a  vibrating  body,  the  pitch 
of  the  note  depends  upon  the  rate  of  vibration  of  the  body. 

387.  The  Doppler  effect.  When  a  rapidly  moving  express  train  rushes 
past  an  observer,  he  notices  a  very  distinct  and  sudden  change  in  the 
pitch  of  the  bell  as  the  engine  passes  him,  the  pitch  being  higher  as 
the  engine  approaches  than  as  it  recedes.  The  explanation  is  as  follows  : 
The  bell  sends  out  pulses  at  exactly  equal  intervals  of  time.    As  the 
train  is  approaching,  however,  the  pulses  reach  the  ear  at  shorter  inter- 
vals than  the  intervals  between  emissions,  since  the  train  comes  toward 
the  observer  between  two  successive  emissions.    But  as  the  train  recedes, 
the  interval  between  the  receipt  of  pulses  by  the  ear  is  longer  than  the 
interval  between  emissions,  since  the  train  is  moving  away  from  the 
ear  during  the  interval  between  emissions.    Hence  the  pitch  of  the  bell 
is  higher  during  the  approach  of  the  train  than  during  its  recession. 
This  phenomenon  of  the  change  in  pitch  of  a  note  proceeding  from  an 
approaching  or  receding  body  is  known  as  the  Doppler  effect. 

388.  Loudness.    The  loudness  or  intensity  of  a  sound  de- 
pends upon  the  rate  at  Avhich  energy  is  communicated  by  it 
to  the  tympanum  of  the  ear.    Loudness  is  therefore  determined 
by  the  distance  of  the  source  and  the  amplitude  of  its  vibration. 

If  a  given  sound  pulse  is  free  to  spread  equally  in  all  direc- 
tions, at  a  distance  of  100  feet  from  the  source  the  same  energy 
must  be  distributed  over  a  sphere  of  four  times  as  large  an 
area  as  at  a  distance  of  50  feet.  Hence  under  these  ideal  con- 
ditions the  intensity  of  a  sound  varies  inversely  as  the  square  of 
the  distance  from  the  source.  But  when  sound  is  confined 
within  a  tube  so  that  the  energy  is  continually  communicated 
from  one  layer  to  another  of  equal  area,  it  will  travel  to  great 
distances  with  little  loss  of  intensity.  This  explains  the  effi- 
ciency of  speaking  tubes  and  megaphones. 


REFLECTION  AND  REENFORCEMENT  327 


QUESTIONS  AND  PROBLEMS 

1.  A  thunderclap  was  heard  5J  sec.  after  the  accompanying  light- 
ning flash  was  seen.    How  far  away  did  the  flash  occur,  the  temperature 
at  the  time  being  20°  C.? 

2.  Why  does  the  sound  die  away  very  gradually  after  a  bell  is  struck  ? 

3.  Why  does  placing  the  hand  back  of  the  ear  enable  a  partially 
deaf  person  to  hear  better? 

4.  Explain  the  principle  of  the  ear  trumpet. 

5.  The  vibration  rate  of  a  fork  is  256.    Find  the  wave  length  of  the 
note  given  out  by  it  at  20°  C. 

6.  Since  the  music  of  an  orchestra  reaches  a  distant  hearer  without 
confusion  of  the  parts,  what  may  be  inferred  as  to  the  relative  velocities 
of  the  notes  of  different  pitch  ? 

7.  What  is  the  relation  between  pitch  and  wave  length?    How  is 
this  made  evident  by  the  fact  noted  in  question  6  ? 

8.  If  we  increase  the  .amplitude  of  vibration  of  a  guitar  string,  what 
effect  has  this  upon  the  amplitude  of  the  wave?   upon  the  loudness? 
upon  the  length  of  the  wave  ?  upon  the  pitch  ? 


REFLECTION,  REENFORCEMENT,  AND  INTERFERENCE 

389.  Echo.  That  a  sound  wave  in  hitting  a  wall  suffers 
reflection  is  shown  by  the  familiar  phenomenon  of  echo.  The 
roll  of  thunder  is  due  to  successive  reflections  of  the  original 
sound  from  clouds  and  other  surfaces  which  are  at  different 
distances  from  the  observer. 

In  ordinary  rooms  the  walls  are  so  close  that  the  reflected 
waves  return  before  the  effect  of  the  original  sound  on  the 
ear  has  died  out.  Consequently  the  echo  blends  with  and 
strengthens  the  original  sound  instead  of  interfering  with  it. 
This  is  why,  in  general,  a  speaker  may  be  heard  so  much 
better  indoors  than  in  the  open  air.  Since  the  ear  cannot 
appreciate  successive  sounds  as  distinct  if  they  come  at  inter- 
vals shorter  than  a  tenth  of  a  second,  it  will  be  seen  from  the 
fact  that  sounds  travel  about  113  feet  in  a  tenth  of  a  second 
that  a  wall  which  is  nearer  than  about  50  feet  cannot  possibly 
produce  a  perceptible  echo.  In  rooms  which  are  large  enough 


328      NATURE  AND  TRANSMISSION  OF  SOUND 


FIG.  348.    Sound  foci 


to  give  rise  to  troublesome  echoes  it  is  customary  to  hang 
draperies  of  some  sort,  so  as  to  break  up  the  sound  waves  and 
prevent  regular  reflection. 

390.  Sound  foci.    Let  a  watch  be  hung  at  the  focus  of  a  large  con- 
cave mirror.    On  account  of  the  reflection  from  the  surface  of  the  mirror 
a  fairly  well-defined  beam  of  sound  will 

be  thrown  out  in  front  of  the  mirror, 

so  that  if  both  watch  and  mirror  are 

hung  on  a  single  support  and  the  whole 

turned  in  different  directions  toward  a 

number  of  observers,  the  ticking  will 

be  distinctly  heard  by  those  directly  in  front  of  the  mirror,  but  not  by 

those  at  one  side.    If  a  second  mirror  is  held  in  the  path  of  this  beam, 

as  in  Fig.  348,  the  sound  may  be  again  brought  to  a  focus,  so  that  if  the 

ear  is  placed  in  the  focus  of  this  second  mirror,  or,  better  still,  if  a  small 

funnel  which  is  connected  with  the  ear  by  a  rubber  tube  is  held  in  this 

focus,  the  ticking  of  the  watch  may  sometimes  be  heard  hundreds  of  feet 

away.  A  whispering  gallery  is  a  room  so  arranged       c=3_ 

as  to  contain  such  sound  foci.    Any  two  opposite 

points  a  few  feet  from  the  walls  of  a  dome,  like 

that  of  St.  Peter's  at  Rome  or  St.  Paul's  at  London, 

are  sufficiently  near  to  such  sound  foci  to  make 

very  low  whispers  on  one  side  distinctly  audible  at 

the    other,  although  at  intermediate  points  no 

sound  can  be  heard.    There  are  well-known  sound 

foci  under  the  dome  of  the  Capitol  at  Washington 

and  in  the  Mormon  Tabernacle  at  Salt  Lake  City. 

391.  Resonance.   Resonance  is  the  reen- 
forcement  or  intensification  of  sound  because 

of  the  union  of  direct  and  reflected  waves. 

Thus,  let  one  prong  of  a  vibrating  tuning 
fork,  which  makes,  for  example,  512  vibrations 
per  second,  be  held  over  the  mouth  of  a  tube 
an  inch  or  so  in  diameter,  arranged  as  in  Fig.  349,  so  that  as  the  vessel 
A  is  raised  or  lowered,  the  height  of  the  water  in  the  tube  may  be  ad- 
justed at  will.  It  will  be  found  that  as  the  position  of  the  water  is 
slowly  lowered  from  the  top  of  the  tube  a  very  marked  reenforcement 
of  the  sound  will  occur  at  a  certain  point. 


FIG.  349.   Illustrating 
resonance 


REFLECTION  AND  REENFORCEMENT 


329 


Let  other  forks  of  different  pitch  be  tried  in  the  same  way.  It  will 
be  found  that  the  lower  the  pitch  of  the  fork,  the  lower  must  be  the 
water  in  the  tube  in  order  to  get  the  best  reinforcement.  This  means 
that  the  longer  the  wave  length  of  the  note  which  the  fork  produces, 
the  longer  must  be  the  air  column  in  order  to  obtain  resonance. 

We  conclude,  therefore,  that  a  fixed  relation  exists  between 
the  wave  length  of  a  note  and  the  length  of  the  air  column  which 
will  reenforce  it. 

392.  Best  resonant  length  of  a  closed  pipe  is  one-fourth  wave 
length.  If  we  calculate  the  wave  length  of  the  note  of  the 
fork  by  dividing  the  speed  of  sound  by  the  vibration  rate  of 
the  fork,  we  shall  find  that,  in  every  case,  the 
length  of  air  column  which  gives  the  best  response 
is  approximately  one-fourth  wave  Ie7igth.  The 
reason  for  this  is  evident  when  we  consider 
that  the  length  must  be  such  as  to  enable  the 
reflected  wave  to  return  to  the  mouth  just  in 
time  to  unite  with  the  direct  wave  which  is  at 
that  instant  being  sent  off  by  the  prong.  Thus, 
when  the  prong  is  first  starting  down  from  the 
position  A  (see  Fig.  350),  it  starts  the  begin- 
ning of  a  condensation  down  the  tube.  If  this 
motion  is  to  return  to  the  mouth  just  in  time  FlG  359 


to  unite  with  the  direct  wave  sent  off  by  the  nant  length  of  a 
prong,  it  must  get  back  at  the  instant  the  prong  closed  PlPe 
is  starting  up  from  the  position  C.  In  other 
words,  the  pulse  must  go  down  the  tube  and  come  back  again 
while  the  prong  is  making  a  half  vibration.  This  means  that 
the  path  down  and  back  must  be  a  half  wave  length,  and  hence 
that  the  length  of  the  tube  must  be  a  fourth  of  a  wave  length. 
From  the  above  analysis  it  will  appear  that  there  should 
also  be  resonance  if  the-  reflected  wave  does  not  return  to  the 
mouth  until  the  fork  is  starting  back  its  second  time  from  (7, 
that  is,  at  the  end  of  one  and  a  half  vibrations  instead  of  a 


330      NATUKE  AND  TRANSMISSION  OF  SOUND 

half  vibration.  The  distance  from  the  fork  to  the  water  and 
back  would  then  be  one  and  a  half  "wave  lengths;  that  is,  the 
water  surface  would  be  a  half  wave  length  farther  down  the 
tube  than  at  first.  The  tube  length  would  therefore  now  be 
three  fourths  of  a  wave  length. 

Let  the  experiment  be  tried.  A  similar  response  will  indeed  be 
found,  as  predicted,  a  half  wave  length  farther  down  the  tube.  This 
response  will  be  somewhat  weaker  than  before,  as  the  wave  has  lost 
some  of  its  energy  in  traveling  a  long  distance  through  the  tube.  It 
may  be  shown  in  a  similar  way  that  there  will  be  resonance  where  the 
tube  length  is  f ,  J,  or  indeed  any  odd  number  of  quarter  wave  lengths; 

393.  Best  resonant  length  of  an  open  pipe  is  one-half  wave 
length.    Let  the  same  tuning  fork  which  was  used  in  §  392  be  held  in 
front  of  an  open  pipe  (8  or  10  inches 
long)  the  length  of  which  is  made  ad- 
justable by  slipping  back  and  forth  over 
it  a  tightly  fitting  roll  of  writing  paper     ^  ^    Resonant  lengtfa  of  an 
(Fig.  35*)..  It  will  be  found  that  for  one          Qpen  pipe  is  ^  waw  ^ngth 
particular  length  this  open  pipe  will  re- 
spond quite  as  loudly  as  did  the  closed  pipe,  but  the  responding  length 
will  be  found  to  be  just  twice  as  great  as  before.    Other  resonant  lengths 
can  be  found  when  the  tube  is  made  2,  3,  etc.  times  as  long. 

We  learn,  then,  that  the  shortest  resonant  length  of  an  open 
pipe  is, one-half  wave  length,  and  that  there  is  resonance  at  any 
multiple  of  a  half  wave  length. 

The  fact  that  the  shortest  resonant  length  of  the  open  pipe 
is  just  twice  that  of  the  closed  one  is  the  experimental  proof 
that  a  condensation,  upon  reaching  the  open  end  of  a  pipe,  is 
reflected  as  a  rarefaction.  This  means  that  when  the  lower 
end  of  the  tube  of  Fig.  350  is  open,  a  condensation  upon 
reaching  it  suddenly  expands.  In  consequence  of  this  expan- 
sion the  new  pulse  which  begins  at  this  instant  to  travel  back 
through  the  tube  is  one  in  which  the  particles  are  moving 
down  instead  of  up;  that  is,  the  particles  are  moving  in  a 
direction  opposite  to  that  in  which  the  wave  is  traveling. 
This  is  always  the  case  in  a  rarefaction  (see  Fig.  344).  In 


REFLECTION  AND  REENFORCEMENT  331 

order  then  to  unite  with  the  motion  of  the  prong  this  down- 
ward motion  of  the  particles  must  get  back  to  the  mouth 
when  the  prong  is  just  starting  down  from  A  the  second  time ; 
that  is,  after  one  complete  vibration  of  the  prong.  This  shows 
why  the  pipe  length  is  one-half  wave  length. 

394.  Resonators.    If  the  vibrating  fork  at  the  mouth  of  the 
tubes  in  the  preceding  experiments  is  replaced  by  a  train  of 
ivaves  coming  from  a  distant  source,  precisely  the  same  analysis 
leads  to  the  conclusion  that  the  waves  reflected  from  the  bottom 
of  the  tube  will  reenforce  the  oncoming  waves  when  the  length 
of  the  tube  is  any  odd  number  of  quarter  wave  lengths  in  the 
case  of  a  closed  pipe,  or  any  number  of  half  wave  lengths  in  the 
case  of  an  open  pipe.   It  is  clear,  therefore,  that  every  air  cham- 
ber will  act  as  a  resonator  for  trains  of  waves  of  a  certain  wave 
length.    This  is  why  a  conch  shell  held  to  the  ear  is  always 
heard  to  hum  with  a  particular  note.    Feeble  waves  which  pro- 
duce no  impression  upon  the  unaided  ear  gain  sufficient  strength 
when  reenforced  by  the  shell  to  become  audible.    When  the  air 
chamber  is  of  irregular  form  it  is  not  usually  possible  to  calcu- 
late to  just  what  wave  length  it  will  respond,  but  it  is  always 
easy  to  determine  experimentally  what  particular  wave  length 
it  is  capable  of  reenforcing.    The  resonators  on  which  tuning 
forks  are  mounted  are  air  chambers  which  are  of  just  the  right 
dimensions  to  respond  to  the  note  given  out  by  the  fork. 

395.  Forced  vibrations ;  sounding  boards.    Let  a  tuning  fork 

be  struck  and  h«ld  in  the  hand.  The  sound  will  be  entirely  inaudible 
except  to  those  quite  near.  Let  the  base  of  the  sounding  fork  be  pressed 
firmly  against  the  table.  The  sound  will  be  found  to  be  enormously 
intensified.  Let  another  sounding  fork  of  different  pitch  be  held  against 
the  same  table.  Its  sound  will  also  be  reenforced.  In  this  case,  then,  the 
table  intensifies  the  sound  of  any  fork  which  is  placed  against  it,  while 
an  air  column  of  a  certain  size  could  intensify  only  a  single  note. 

The  cause  of  the  response  in  the  two  cases  is  wholly  differ- 
ent.  In  the  last  case  the  vibrations  of  the  fork  are  transmitted 


332      NATURE  AND  TRANSMISSION  OF  SOUND 

through  its  base  to  the  table  top  and  force  the  latter  to  vibrate 
in  its  own  period.  The  vibrating  table  top,  on  account  of  its 
large  surface,  sets  a  comparatively  large  mass  of  air  into  motion 
and  therefore  sends  a  wave  of  great  intensity  to  the  ear,  while 
the  fork  alone,  with  its  narrow  prongs,  was  not  able  to  impart 
much  energy  to  the  air.  Vibrations  like  those  of  the  table  top 
are  called  forced  because  they  can  be  produced  with  any  fork, 
no  matter  what  its  period.  Sounding  boards  in  pianos  and 
other  stringed  instruments  act  precisely  as  does  the  table  top 
in  this  experiment  ;  that  is,  they  are  set  into  forced  vibrations 
by  any  note  of  the  instrument  and  reenforce  it  accordingly. 

396.  Beats.  Since  two  sound  waves  are  able  to  unite  so  as 
to  reenforce  each  other,  it  ought  also  to  be  possible  to  make 
them  unite  so  as  to  interfere  with  or  destroy  each  other.  In 
other  words,  under  the  proper  conditions  the  union  of  two 
sounds  ought  to  produce  silence. 

Let  two  mounted  tuning  forks  of  the  same  pitch  be  set  side  by  side, 
as  in  Fig.  352.  Let  the  two  forks  be  struck  in  quick  succession  with  a 
soft  mallet,  for  example,  a  rubber  stopper  on  the  end  of  a  rod.  The  two 
notes  will  blend  and  produce  a  smooth,  even  tone.  Then  let  a  piece  of  wax 
or  a  small  coin  be  stuck  to  a  prong 
of  one  of  the  forks.  This  dimin- 
ishes slightly  the  number  of  vibra- 
tions which  this  fork  makes  per 
second,  since  it  increases  its  mass. 


Again,  let  the  two  forks  be  sounded        FlG'  352'    A™int  °£ 


together.  The  former  smooth  tone 
will  be  replaced  by  a  throbbing  or  pulsating  one.  This  is  due  to  the 
alternate  destruction  and  reenforcement  of  the  sounds  produced  by 
the  two  forks.  This  pulsation  is  called  the  phenomenon  of  beats. 

The  mechanism  of  the  alternate  destruction  and  reenforce- 
ment may  be  understood  from  the  following.  Suppose  that  one 
fork  makes  256  vibrations  per  second  (see  the  dotted  line  AC 
in  Fig.  353),  while  the  other  makes  255  (see  the  heavy  line 
AC).  If  at  the  beginning  of  a  given  second  the  two  forks 


REFLECTION  AND  KEENFORCEMENT  333 

are  swinging  together,  so  that  they  simultaneously  send  out 
condensations  to  the  observer,  these  condensations  will  of 
course  unite  so  as  to  produce  a  double  effect  upon  the  ear 
(see  A',  Fig.  353).  Since  now  one  fork  gains  one  complete 
vibration  per  second  over  the  other,  at  the  end  of  the  second 
considered  the  two  forks  A  EC 

will    again    be    vibrating       \f\[f^^ 
together,  that  is,  sending     A>  B.  Q. 

out   condensations  which 
add  their  effects  as  before 

("see  C'\    In  the  middle  of  ,  , 

FIG.  353.    Graphical  illustration  of  beats 

this  second,  however,  the 

two  forks  are  vibrating  in  opposite  directions  (see  .ZT);  that 
is,  one  is  sending  out  rarefactions  while  the  other  sends  out 
condensations.  At  the  ear  of  the  observer  the  union  of  the 
rarefaction  (backward  motion  of  the  air  particles)  produced 
by  one  fork  with  the  condensation  (forward  motion)  pro- 
duced by  the.  other  results  in  no  motion  at  all,  provided  the 
two  motions  have  the  same  energy ;  that  is,  in  the  middle  of  the 
second  the  two  sounds  have  united  to  produce  silence  (see  B').  It 
will  be  seen  from  the  above  that  the  number  of  beats  per  second 
is  equal  to  the  difference  in  the  vibration  numbers  of  the  two  forks. 

To  test  this  conclusion,  let  more  wax  or  a  heavier  coin  be  added  to 
the  weighted  prong ;  the  number  of  beats  per  second  will  be  increased. 
Diminishing  the  weight  will  reduce  the  number  of  beats  per  second. 

In  tuning  a  piano  the  double  and  triple  strings  are  brought 
into  unison  by  tuning  so  as  to  eliminate  beats. 

397.  Interference  of  sound  waves  by  reflection.  Let  a  thin 
cork  about  an  inch  in  diameter  be  attached  to  one  end  of  a  brass  rod 
from  one  to  two  meters  long.  Let  this  rod  be  clamped  firmly  in  the 
middle,  as  in  Fig.  354.  Let  a  piece  of  glass  tubing  a  meter  or  more 
long  and  from  an  inch  to  an  inch  and  a  half  in  diameter  be  slipped  over 
the  cork,  as  shown.  Let  the  end  of  the  rod  be  stroked  longitudinally  with 
a  well-resined  cloth.  A  loud,  shrill  note  will  be  produced. 


334      NATURE  AND  TRANSMISSION  OF  SOUND 

This  note  is  due  to  the  fact  that  the  slipping  of  the  resined  cloth 
over  the  surface  of  the  rod  sets  the  latter  into  longitudinal  vibrations, 
so  that  its  ends  impart  alternate  condensations  and  rarefactions  to  the 
layers  of  air  in  contact  with  them.  As  soon  as  this  note  is  started 


FIG.  354.    Interference  of  advancing  and  retreating  trains  of  sound  waves 

the  cork  dust  inside  the  tube  will  be  seen  to  be  intensely  agitated.  If  the 
effect  is  not  marked  at  first,  a  slight  slipping  of  the  glass  tube  forward 
or  back  will  bring  it  out.  Upon  examination  it  will  be  seen  that  the 
agitation  of  the  cork  dust  is  not  uniform,  but  at  regular  intervals 
throughout  the  tube  there  will  be  regions  of  complete  rest,  nA,  rc2,  ns, 
etc.,  separated  by  regions  of  intense  motion. 

The  points  of  rest  correspond  to  the  positions  in  which  the 
reflected  train  of  sound  waves  returning  from  the  end  of  the 
tube  neutralizes  the  effect  of  the  advancing  train  passing  down 
the  tube  from  the  vibrating  rod.  The  points  of  rest  are  called 
nodes,  the  intermediate  ^  a3  az  % 

portions    loops  or  anti-     *==QR      I  I  I  II 

j  TU/       v  4.  n*      n&      n*       n* 

nodes.       1  ne     distance 

between  these  nodes  is     FlG' 355'  ^tance  between  nodes  is  one-half 

1.     1£  1        ^    £  WaVG  len£th 

one-half  wave  length,  for 

at  the  instant  that  the  first  wave  front  «1  (Fig.  355)  reaches  the 
end  of  the  tube  it  is  reflected  and  starts  back  toward  R.  Since 
at  this  instant  the  second  wave  front  #2  is  just  one  wave  length 
to  the  left  of  a^  the  two  wave  fronts  must  meet  each  other  at 
a  point  w  ,  just  one-half  wave  length  from  the  end  of  the  tube. 
The  exactly  equal  and  opposite  motions  of  the  particles  in  the 
two  wave  fronts  exactly  neutralize  each  other.  Hence  the  point 
n^  is  a  point  of  no  motion,  that  is,  a  node.  Again,  at  the  in- 
stant that  the  rejected  wave  front  a^  met  the  advancing  wave 
front  #2  at  »1?  the  third  wave  front  a8  was  just  one  wave  length 
to  the  left  of  n  Hence,  as  the  first  wave  front  a^  continues 


REFLECTION  AND  KEENFOKCEMENT  335 

to  travel  back  toward  R  it  meets  ag  at  n^  just  one-half  wave 
length  from  n^  and  produces  there  a  second  node.  Similarly, 
a  third  node  is  produced  at  n^  one-half  wave  length  to  the 
left  of  n^  etc.  Thus  the  distance  between  two  nodes  must  always 
be  just  one  lialf  the  wave  length  of  the  waves  in  the  train. 

In  the  preceding  discussion  it  has  been  tacitly  assumed  that  the  two 
oppositely  moving  waves  are  able  to  pass  through  each  other  without 
either  of  them  being  modified  by  the  presence  of  the  other.  That  two 
opposite  motions  are,  in  fact,  transferred  in  just  this  manner  through  a 
medium  consisting  of  elastic  particles  may  be  beautifully  shown  by  the 
following  experiment 
with  the  row  of  balls 
used  in  §  380. 

Let  the  ball  at  one  end  FIG.  356.   Nodes  and  loops  in  a  cord 

of  the  row  be  raised  a 

Black  line  denotes  advancing  tram  ;  dotted  line, 
distance  of,  say,  2  inches  reflected  train 

and  the  ball  at  the  other 

end  raised  a  distance  of  4  inches.  Then  let  both  balls  be  dropped 
simultaneously  against  the  row.  The  two  opposite  motions  will  pass 
through  each  other  in  the  row  altogether  without  modification,  the 
larger  motion  appearing  at  the  end  opposite  to  that  at  which  it  started, 
and  the  smaller  likewise. 

Another  and  more  complete  analogy  to  the  condition  existing  within 
the  tube  of  Fig.  354  may  be  had  by  simply  vibrating  one  end  of  a 
two-  or  three-meter  rope,  as  in  Fig.  356.  The  trains  of  advancing  and 
reflected  waves  which  continuously  travel  through  each  other  up  and 
down  the  rope  will  unite  so  as  to  form  a  series  of  nodes  and  loops.  The 
nodes  at  c  and  e  are  the  points  at  which  the  advancing  and  reflected 
waves  are  always  urging  the  cord  equally  in  opposite  directions.  The 
distance  between  them  is  one  half  the  wave  length  of  the  train  sent 
down  the  rope  by  the  hand. 

QUESTIONS  AND  PROBLEMS 

1.  Account  for  the  sound  produced  by  blowing  across  the  mouth  of 
an  empty  bottle.    The  bottle  may  be  tuned  to  different  pitches  by  add- 
ing more  or  less  water.   Explain. 

2.  Explain  the  roaring  sound  heard  when  a  sea  shell,  a  tumbler,  or 
an  empty  tin  caa  is  held  to  the  ear. 


336      NATURE  AND  TRANSMISSION  OF  SOUND 

3.  Find  the  number  of  vibrations  per  second  of  a  fork  which  produces 
resonance  in  a  closed  pipe  1  ft.  long  ;  in  an  open  pipe  1  ft.  long*.   (Take 
the  speed  of  sound  as  1120  ft.  per  second.) 

4.  A  gunner  hears  an  echo  5^  sec.  after  he  fires.    How  far  away  was 
the  reflecting  surface,  the  temperature  of  the  air  being  20°  C.? 

5.  The  shortest  closed  air  column  that  gave  resonance  with  a  tuning 
fork  was  32  cm.    Find  the  rate  of  the  fork  if  the  velocity  of  sound  was 
340  meters  per  second.  -• 'i  - 

6.  A  tuning  fork  gives  strong  resonance  when  held  on  its  flat  side  or 
on  its  edge,  but  when  held  cornerwise  over  the  air  column  the  resonance 
ceases.    Explain. 

7.  What  is  meant  by  the  phenomenon  of  beats  in  sound?   How  may 
it  be  produced,  and  what  is  its  cause  ? 

8.  What  is  the  length  of  the  shortest  closed  tube  that  will  act  as  a 
resonator  to  a  fork  whose  rate  is  427  per  second  ?  (Temperature  =  20°  C.) 

9.  A  fork  making  500  vibrations  per  second  is  found  to  produce 
resonance  in  an  air  column  like  that  shown  in  Fig.  349,  first  when  the 
water  is  a  certain  distance  from  the  top,  and  again  when  it  is  34  cm. 
lower.    Find  the  velocity  of  sound. 

10.  Show  why  an  open  pipe  needs  to  be  twice  as  long  as  a  closed 
pipe  if  it  is  to  respond  to  the  same  note. 


CHAPTER  XVII 


PROPERTIES  OF  MUSICAL  SOUNDS 

MUSICAL  SCALES 
398.  Physical  basis  of  musical  intervals.   Let  a  metal  or  card 

board  disk  10  or  12  inches  in  diameter  be  provided  with  four  concentric 
rows  of  equidistant  holes,  the  successive  rows  containing  respectively 
24,  30,  36,  and  48  holes  (Fig.  357).  The  holes  should  be  about  J  inch 
in  diameter,  and  the  rows  should  be  about 
\  inch  apart.  Let  this  disk  (a  siren)  be 
placed  in  the  rotating  apparatus  and  a 
constant  speed  imparted.  Then  let  a  jet 
of  air  be  directed,  as  in  §  385,  against  each 
row  of  holes  in  succession.  It  will  be  found 
that  the  musical  sequence  do,  mi,  sol,  do" 
results.  If  the  speed  of  rotation  is  in- 
creased, each  note  will  rise  in  pitch,  but 
the  sequence  will  remain  unchanged. 

We  learn,  therefore,  that  the  musical  FIG.  357.  Siren  for  produc- 
sequence  do,  mi,  sol,  do'  consists  of  notes  inS  musical^sequence  do,  mi, 
whose  vibration  numbers  have  the  ratios 

of  24,  30,  36,  and  48,  that  is,  4,  5,  6,  8,  and  that  this  sequence 
is  independent  of  the  absolute  vibration  numbers  of  the  tones. 

Furthermore,  when  two  notes  an  octave  apart  are  sounded 
together,  they  form  the  most  harmonious  combination  which  it 
is  possible  to  obtain.  These  characteristics  of  notes  an  octave 
apart  were  recognized  in  the  earliest  times,  long  before  any- 
thing whatever  was  known  about  the  ratio  of  their  vibration 
numbers.  The  preceding  experiment  showed  that  this  ratio 
is  the  simplest  possible,  namely,  24  to  48,  or  1  to  2.  Again, 
the  next  easiest  musical  interval  to  produce,  and  the  next 

337 


338  PROPERTIES  OF  MUSICAL  SOUNDS 

most  harmonious  combination  which  can  be  found,  corre- 
sponds to  the  two  notes  commonly  designated  as  do,  sol  Our 
experiment  showed  that  this  interval  corresponds  to  the  next 
simplest  possible  vibration  ratio,  namely,  24  to  36,  or  2  to  3. 
When  sol  is  sounded  with  do',  the  vibration  ratio  is  seen  to  be 
36  to  48,  or  3  to  4.  We  see,  therefore,  that  the  three  simplest 
possible  ratios  of  vibration  numbers,  namely,  1  to  2,  2  to  3, 
and  3  to  4,  are  used  in  the  production  of  the  three  no  tea 
do,  sol,  do'.  Again,  our  experiment  shows  that  another  har- 
monious musical  interval,  do,  mi,  corresponds  to  the  vibration 
ratio  24  to  30,  or  4  to  5.  We  learn,  therefore,  that  harmonious 
musical  intervals  correspond  to  very  simple  vibration  ratios. 

399.  The  major  diatonic  scale.  When  the  three  notes  do, 
mi,  sol,  which,  as  seen  above,  have  the  vibration  ratios  4,  5,  6, 
are  all  sounded  together,  they  form  a  remarkably  pleasing 
combination  of  tones.  This  combination  was  picked  out  and 
used  very  early  in  the  musical  development  of  the  race.  It  is 
now  known  as  the  major  chord.  The  major  diatonic  scale  is 
built  up  of  three  major  chords  in  the  manner  shown  in  the 
following  table,  where  the  first  major  chord  is  denoted  by  1, 
the  second  by  2,  and  the  third  by  3. 

Syllables do      re      mi     fa      sol      la,      si     do  re 

Letters CD       E      F       G      A     B      C'  D' 

Relative  vibration  numbers  .    .    24     27      30     32      36     40    45      48  54 

111 

22  2 
333 

The  chords  do-mi-sol  (the  tonic),  sol-si-re  (the  dominant), 
and  fa-la-do  (the  subdominant)  occur  frequently  in  all  music. 

Standard  middle  C  forks  made  for  physical  laboratories 
all  have  the  vibration  number  256,  which  makes  A  in  the 
physical  scale  426J.  In  the  so-called  international  pitch  A 
has  435  vibrations,  and  in  the  widely  adopted  American 
Federation  of  Musicians'  pitch,  440. 


VIBRATING  STRINGS  339 

400.  The  even-tempered  scale.    If  G-  is  taken  as  do,  and  a 
scale  built  up  as  above,  it  will  be  found  that  six  of  the  above 
notes  in  each  octave  can  be  used  in  this  new  key,  but  that  two 
additional  ones  are  required  (see  table  below).    Similarly,  to 
build  up  scales,  as  above,  in  all  the  keys  demanded  by  modern 
music  would  require  about  fifty  notes  in  each  octave.    Hence 
a  compromise  is  made  by  dividing  the  octave   into  twelve 
equal  intervals  represented  by  the  eight  white  arid  five  black 
keys  of  a  piano.    How  much  this  so-called  even-tempered  scale 
differs  from  the  ideal,  or  diatonic,  scale  is  shown  below. 

Note  C      D         E         F        G  A  R  C'     D'  E'  F'  G' 

Diatonic  ....  256   288       320       341£  384  426|  480  512  576  640  682.2  768 

Diatonic  key  of  G 384  433  480  512  576  640  720  768 

Tempered    ...  256   287.4   322.7    341.7  383.8  430.7  483.5  512  574.8  645.4  683.4  767.6 

VIBRATING  STRINGS* 

401 .  Laws  of  vibrating  strings.  Let  two  piano  wires  be  stretched 
over  a  box  or  a  board  with  pulleys  attached  so  as  to  form  a  sonometer 
(Fig.  358).    Let  the  weights  A  and  B  be  adjusted  until  the  two  wires 
emit    exactly    the    same 

note.  The  phenomenon 
of  beats  will  make  it 
possible  to  do  this  with  Afi 

great  accuracy    Then  let        ^  ^  ^  The  gonometer 

the  bridge  D  be  inserted 
^exactly  at  the  middle  of  one  of  the  wires,  and  the  two  wires  plucked  in 
succession.  The  interval  will  be  recognized  at  once  as  do,  do'.  Next  let 
the  bridge  be  inserted  so  as  to  make  one  wire  two  thirds  as  long  as  the 
other,  and  let  the  two  be  plucked  again.  The  interval  will  be  recognized 
as  do,  s#L 

Now  it  was  shown  in  §  398  that  do1  has  twice  as  many 
vibrations  per  second  as  do,  and  sol  has  three  halves  as  many. 
Hence,  since  the  length  corresponding  to  do'  is  one  half  as 
great  as  the  first  length,  and  that  corresponding  to  sol  two  thirds 

*This  discussion  should  be  followed  by  a  laboratory  experiment  on  the 
laws  of  vibrating  strings.  See,  for  example,  Experiment  41  of  the  authors1 
Manual. 


340  PROPERTIES  OF  MUSICAL  SOUNDS 

as  great,  we  conclude  from  this  experiment  that,  other  things 
being  equal,  the  vibration  numbers  of  strings  are  inversely 
proportional  to  their  lengths. 

Again,  let  the  two  wires  be  tuned  to  unison,  and  then  let  the  weight 
A  be  increased  until  the  pull  which  it  exerts  on  the  wire  is  exactly  four 
times  as  great  as  that  exerted  by  B.  The  note  given  out  by  the  A  wire 
will  again  be  found  to  be  an  octave  above  that  given  out  by  the  B  wire. 

We  learn,  then,  that  the  vibration  numbers  of  similar  strings  of 
equal  length  are  proportional  to  the  square  roots  of  their  tensions. 

In  stringed  instruments,  for  example  the  piano,  the  differ- 
ent pitches  are  obtained  by  using  strings  of  different  length, 
tension,  and  mass  per  unit  length. 

402.  Nodes  and  loops  in  vibrating  strings.    Let  a  string  a  meter 

long  be  attached  to  one  of  the  prongs  of  a  large  tuning  fork  which  makes 

in    the    neighborhood    of 

100  vibrations  per  second. 

Let  the  other  end  be  at- 

tached   as   in    the    figure 

and  the  fork  set  into  vi-     ^      FlG.  359.    string  vibrating  as  a  whole 

bration.   If  the  fork  is  not 

electrically  driven,  which  is  much  to  be  preferred,  it  may  be  bowed 

with  a  violin  bow  or  struck  with  a  soft  mallet.    By  making  the  tension 

of  the  thread,  for  example,  proportional  to  the  numbers  9,  4,  and  1  it 

will  be  found  possible  to  make  it  vibrate  either  as  a  whole,  as  in  Fig.  359, 

or  in  two  or  three  parts 

(Fig.  360), 

This  effect  is  due,  as 
explained  in  §  397,  to  FlG*  36°-    String  vibrating  in  three 

„  G^  segments 

the  interference  of  the 

direct  and  reflected  waves  sent  down  the  string  from  the 
vibrating  fork.  But  we  shall  show  in  the  next  paragraph 
that  in  considering  the  effects  of  the  vibrating  string  on 
the  surrounding  air  we  shall  make  no  mistake  if  we  think  of 
it  as  clamped  at  each  node,  and  as  actually  vibrating  in  two 
or  three  or  four  separate  parts,  as  the  case  may  be. 


FUNDAMENTALS  AND  OVERTONES  341 

FUNDAMENTALS  AND  OVERTONES 

403.  Fundamentals  and  overtones.  If  the  assertion  just 
made  be  correct,  then  a  string  which  has  a  node  in  the  middle 
communicates  to  the  air  twice  as  many  pulses  per  second  as 
the  same  string  when  it  vibrates  as  a  whole.  This  may  be 
conclusively  shown  as  follows : 

Let  the  sonometer  wire  (Fig.  358)  be  plucked  in  the  middle  and  the 
pitch  of  the  corresponding  tone  carefully  noted.  Then  let  the  finger 
be  touched  to  the  middle  of  the  wire,  and  the  latter  plucked  midway 
between  this  point  and  the  end.*  .  The  octave  of  the  original  note  will 
be  distinctly  heard.  Next  let  the  finger  be  touched  at  a  point  one  third 
of  the  wire  length  from  one  end,  and  the  wire  again  plucked.  The  note 
will  be  recognized  as  .so/'.  Since  we  learned  in  §  399  that  sol'  has  three 
halves  as  many  vibrations  as  do',  it  must  have  three  times  as  many 
vibrations  as  the  original  note.  Hence  a  wire  which  is  vibrating  in 
three  segments  sends  out  three  times  as  many  vibrations  as  when  it  is 
vibrating  as  a  whole. 

When  a  wire  vibrates  simply  as  a  whole,  it  gives  forth  the 
lowest  note  which  it  is  capable  of  producing.  This  note  is 
called  the  fundamental  or  first  partial  of  the  wire.  When  the 
wire  is  made  to  vibrate  in  two  parts,  it  gives  forth,  as  has  just 
been  shown,  a  note  an  octave  higher  than  the  fundamental. 
This  is  called  the  first  overtone  or  second  partial.  When  the 
wire  is  made  to  vibrate  in  three  parts  it  gives  forth  a  note  cor- 
responding to  three  times  the  vibration  number  of  the  funda- 
mental, namely,  sol'.  This  is  called  the  second  overtone  or  third 
partial.  When  the  wire  vibrates  in  four  parts,  it  gives  forth  the 
third  overtone,  which  is  two  octaves  above  the  fundamental. 
The  overtones  of  wires  are  often  called  harmonics.  They  bear 
the  vibration  ratios  2,  3,  4,  5,  6,  7,  etc.  to  the  fundamental.! 

*  It  is  well  to  remove  the  finger  almost  simultaneously  with  the  plucking. 

t  Some  instruments,  such  as  bells,  can  produce  higher  tones  whose  vibra- 
tion numbers  are  not  exact  multiples  of  the  fundamental.  These  notes  are 
still  called  overtones,  but  they  are  not  called  harmonics,  the  latter  term  being 
reserved  for  the  multiples.  Strings  produce  harmonics  only. 


342  PROPERTIES  OF  MUSICAL  SOUNDS 

404.  Simultaneous  production  of  fundamentals  and  overtones. 
Thus  far  we  have  produced  overtones  only  by  forcing  the  wire 
to  remain  at  rest  at  properly  chosen  points  during  the  bowing. 

Now  let  the  wire  be  plucked  at  a  point  one  fourth  of  its  length  from 
one  end,  without  being  touched  in  the  middle.  The  tone  most  distinctly 
heard  will  be  the  fundamental ;  but  if  the  wire  is  now  touched  very 
lightly  exactly  in  the  middle,  the  sound,  instead  of  ceasing  altogether, 
will  continue,  but  the  note  heard  will  be  an  octave  higher  than  the 
fundamental,  showing  that  in  this  case  there  was  superposed  upon 
the  vibration  of  the  wire  as  a  whole  a  vibration  in  two  segments  also 
(Fig.  361).  By  touching  the 
wire  in  the  middle  the  vibra- 
tion as  a  whole  was  destroyed, 
but  that  in  two  parts  re- 
mained. Let  the  experiment 
be  repeated,  with  this  differ-  FIG.  361.  A  wire  simultaneously  emitting 
ence,  that  the  wire  is  now  its  fundamental  and  first  overtone 

plucked  in  the  middle  instead 

of  one  fourth  its  length  from  one  end.  If  it  is  now  touched  in  the 
middle,  the  sound  will  entirely  cease,  showing  that  when  a  wire  is 
plucked  in  the  middle  there  is  no  first  overtone  superposed  upon  the 
fundamental.  Let  the  wire  be  plucked  again  one  fourth  of  its  length 
from  one  end  and  careful  attention  given  to  the  compound  note  emitted. 
It  will  be  found  possible  to  recognize  both  the  fundamental  and  the 
first  overtone  sounding  at  the  same  time.  Similarly,  by  plucking  at  a 
point  one  sixth  of  the  length  of  the  wire  from  one  end,  and  then  touching 
it  at  a  point  one  third  of  its  length  from  the  end,  the  second  overtone 
may  be  made  to  appear  distinctly,  and  a  trained  ear  will  detect  it  in  the 
note  given  off  by  the  wire,  even  before  the  fundamental  is  suppressed 
by  touching  at  the  point  indicated. 

The  experiments  show,  therefore,  that  in  general  the  note 
emitted  by  a  string  plucked  at  random  is  a  complex  one,  consist- 
ing of  a  fundamental  and  several  overtones,  and  that  just  what 
overtones  are  present  in  a  given  case  depends  on  where  and  how 
the  wire  is  plucked. 

405.  Quality.    Let   the  sonometer  wire  be  plucked  first   in  the 
middle  and  then  close  to  one  end.    The  two  notes  emitted  will  have 
exactly  the  same  pitch,  and  they  may  have  exactly  the  same  loudness, 


FUNDAMENTALS  AND  OVERTONES  343 

but  they  will  be  easily  recognized  as  different  in  respect  to  somethmg 
which  we  call  quality.  The  experiment  of  the  last  paragraph  shows  that 
the  real  physical  difference  in  the  tones  is  a  difference  in  the  sorts  of 
overtones  which  are  mixed  with  the  fundamental  in  the  two  cases. 

Again,  let  a  mounted  Cf  fork  be  sounded  simultaneously  with  a 
mounted  C  fork.  The  resultant  tone  will  sound  like  a  rich,  full  C,  which 
will  change  into  a  hollow  C  when  the  C'  is  quenched  with  the  hand. 

Everyone  is  familiar  with  the  fact  that  when  notes  of  the 
same  pitch  and  londness  are  sounded  upon  a  piano,  a  violin, 
and  a  cornet,  the  three  tones  can  be  readily  distinguished. 
The  last  experiments  suggest  that  the  cause  of  this  difference 
lies  "in  the  fact  that  it  is  only  the  fundamental  which  is  the 
same  in  the  three  cases,  while  the  overtones  are  different.  In 
other  words,  the  characteristic  of  a  tone  which  we  call  its  qual- 
ity is  determined  simply  by  the  number  and  prominence  of  the 
overtones  which  *are  present.  If  the  overtones  present  are  few 
and  weak,  while  the  fundamental  is  strong,  the  tone  is,  as 
a  rule,  soft  and  mellow,  as  when  a  sonometer  wire  is  plucked 
in  the  middle,  or  a  closed  organ  pipe  is  blown  gently,  or  a 
tuning  fork  is  struck  with  a  soft  mallet.  The  presence  of 
comparatively  strong  overtones  up  to  the  fifth  adds  fullness 
and  richness  to  the  resultant  tone.  This  is  illustrated  by  the 
ordinary  tone  from  a  piano,  in  which  several  if  not  all  of  the 
first  five  overtones  have  a  prominent  place.  When  overtones 
higher  than  the  sixth  are  present,  a  sharp  metallic  quality 
begins  to  appear.  This  is  illustrated  when  a  tuning  fork  is 
struck,  or  a  wire  plucked,  with  a  hard  body.  It  is  in  order  to 
avoid  this  quality  that  the  hammers  which  strike  against 
piano  wires  are  covered  with  felt. 

406.  Analysis  of  tones  by  the  manometric  flame.  A  very 
simple  and  beautiful  way  of  showing  the  complex  character 
of  most  tones  is  furnished  by  the  so-called  manometric  flames. 
This  device  consists  of  the  following  parts :  a  chamber  in  the 
block  B  (Fig.  362),  through  which  gas  is  led  by  way  of  the 


344 


PROPERTIES  OF  MUSICAL  SOUNDS 


tubes  C  and  D  to  the  flame  F ;  a  second  chamber  in  the  block 
A,  separated  from  the  first  chamber  by  an  elastic  diaphragm 
made  of  very  thin  sheet  rubber  or  paper,  and  communicating 
with  the  source  of  sound  through  the  tube  E  and  trumpet  G ; 
and  a  rotating  mirror  M  by  which  the  flame  is  observed. 
When  a  note  is  produced  before  the  mouthpiece  G>  the  vibra- 
tions of  the  diaphragm  produce  variations  in  the  pressure  of 


FIG.  362.    Analysis  of  sounds  with  manometric  flames 

the  gas  coming  to  the  flame  through  the  chamber  in  B,  so 
that  when  condensations  strike  the  diaphragm  the  height 
of  the  flame  is  increased,  and  when  rarefactions  strike  it  the 
height  of  the  flame  is  diminished.  If  these  up-and-down 
motions  of  the  flame  are  viewed  in  a  rotating  mirror,  the 
longer  and  shorter  images  of  the  flame,  which  correspond 
to  successive  intervals  of  time,  appear  side  by  side,  as  in 
Fig.  363.  If  a  rotating  mirror  is  not  to  be  had,  a  piece  of 
ordinary  mirror  glass  held  in  the  hand  and  oscillated  back 
and  forth  about  a  vertical  axis  will  be  found  to  give  satis 
factory  results. 


FUNDAMENTALS  AND  OVERTONES 


345 


First  let  the  mirror  be  rotated  when  no  note  is  sounded  before  the 
mouthpiece.  There  will  be  no  fluctuations  in  the  flame,  and  its  image, 
as  seen  in  the  moving  mirror,  will  be  a  straight  band,  as  shown  in  2 
(Fig.  363).  Next  let  a  mounted  C  fork  be  sounded,  or  some  other  simple 
tone  produced  in  front  of  G.  The  image 
in  the  mirror  will  be  that  shown  in  3. 
Then  let  another  fork,  C',  be  sounded 
in  place  of  the  C.  The  image  will  be 
that  shown  in  4.  The  images  of  the 
flame  are  now  twice  as  close  together 
as  before,  since  the  blows  strike  the 
diaphragm  twice  as  often.  Next  let 
the  open  ends  of  the  resonance  boxes 
of  the  tuning  forks  C  and  C'  be  held 
together  in  front  of  G.  The  image  of 
the  flame  will  be  as  shown  in  5.  If 
the  vowel  o  be  sung  in  the  pitch  Bb 
before  the  mouthpiece,  a  figure  exactly 
similar  to  5  will  be  produced,  thus 
showing  that  this  last  note  is  a  com- 
plex, consisting  of  a  fundamental  and 
its  first  overtone. 


<UU.UU.ULL 


FIG.  363.   Vibration  forms  shown 
by  manometric  flames 


The  proof  that  most  other  tones  are  likewise  complex  lies  in 
the  fact  that  when  analyzed  by  the  manometric  flame  they  show 
figures  not  like  3  and  4,  which  correspond  to  simple  tones,  but 
like  5)  6,  and  7,  which  may  be  produced  by  sounding  combina- 
tions of  simple  tones.  In  the  figure,  6  is  produced  by  singing 
the  vowel  e  on  Cu  \  7  is  obtained  when  o  is  sung  on  C".  The 
beautiful  photographs  opposite  page  346,  taken  by  Prof.  D.  C. 
Miller,  show  the  extraordinary  complexity  of  spoken  words. 

407.  Helmholtz's  experiment.  If  the  loud  pedal  on  a  piano  is 
held  down  and  the  vowel  sounds  do,  I,  a,  ah,  e  sung  loudly  into  the  strings, 
these  vowels  will  be  caught  up  and  returned  by  the  instrument  with 
sufficient  fidelity  to  make  the  effect  almost  uncanny. 

It  was  by  a  method  which  may  be  considered  as  merely  a 
refinement  of  this  experiment  that  Helmholtz  proved  conclu- 
sively that  quality  is  determined  simply  by  the  number  and 


346  PROPERTIES  OF  MUSICAL  SOUNDS 

prominence  of  the  overtones  which  are  blended  with  the  fun- 
damental. He  first  constructed  a  large  number  of  resonators, 
like  that  shown  in  Fig.  364,  each  of  which  would  respond  to 
a  note  of  some  particular  pitch.  By  holding 
these  resonators  in  succession  to  his  ear  while 
a  musical  note  was  sounding,  he  picked  out 
the  constituents  of  the  note  ;  that  is,  he  found 
out  just  what  overtones  were  present  and 

what  were  their  relative  intensities.    Then  he    FlG-  364-    Helm- 
,  .  ,  ,  holtz's  resonator 

put  these  constituents  together  and  repro- 
duced the  original  tone.  This  was  done  by  sounding  simul- 
taneously, with  appropriate  loudness,  two  or  more  of  a  whole 
series  of  tuning  forks  which  had  the  vibration  ratios  1,  2,  3, 
4,  5,  6,  7.  In  this  way  he  succeeded  not  only  in  imitating  the 
qualities  of  different  musical  instruments  but  even  in  repro- 
ducing the  various  vowel  sounds. 

408.  Sympathetic  vibrations.  Let  two  mounted  tuning  forks  of 
the  same  pitch  be  placed  with  the  open  ends  of  their  resonators  facing 
eacfy  other.  Let  one  be  set  into  vigorous  vibration  with  a  soft  mallet 
and  then  quickly  quenched  by  grasping  the  prongs  with  the  hand. 
The  other  fork  will  be  found  to  be  sounding  loudly  enough  to  be  heard 
over  a  large  room.  Next  let  a  penny  be  waxed  to  one  prong  of  the  sec- 
ond fork  and  the  experiment  repeated.  When  the  sound  of  the  first 
fork  is  quenched,  no  sound  whatever  will  be  found  to  be  coming  from 
the  second  fork. 

The  experiment  illustrates  the  phenomenon  of  sympathetic 
vibrations,  and  shows  what  conditions  are  essential  to  its  appear- 
ance. If  two  bodies  capable  of  emitting  musical  notes  have 
exactly  the  same  natural  period  of  vibration,  the  pulses  com- 
municated to  the  air  when  one  alone  is  sounding  beat  upon 
the  second  at  intervals  which  correspond  exactly  to  its  own 
natural  period.  Each  pulse,  therefore,  adds  its  effect  to  that  of 
the  preceding  pulses ;  and  though  the  effect  due  to  a  single 
pulse  is  very  slight,  a  great  number  of  such  pulses  produce  a 


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FUNDAMENTALS  AND  OVEKTOKES  347 

large  resultant  effect.  In  the  same  way  a  large  number  of 
very  feeble  pulls  may  set  a  heavy  pendulum  into  vibrations 
of  considerable  amplitude  if  the  pulls  come  at  intervals  exactly 
equal  to  the  natural  period  of  the  pendulum.  On  the  other 
hand,  if  the  two  sounding  bodies  have  even  a  slight  difference 
of  period,  the  effect  of  the  first  pulses  is  neutralized  by  the  ef- 
fect of  succeeding  pulses  as  soon  as  the  two  bodies,  on  account  of 
their  difference  in  period,  get  to  swinging  in  opposite  directions. 

Let  notes  of  different  pitches  be  sung  into  a  piano  when  the  dampers 
are  lifted.  The  wire  which  has  the  pitch  of  the  note  sounded  will  in 
every  case  respond.  Sing  a  little  off  the  key  and  the  response  will  cease. 

409.  Sympathetic  vibrations  produced  by  overtones.    It  is 

not  essential,  in  order  that  a  body  may  be  set  into  sympathetic 
vibrations,  that  it  have  the  same  pitch  as  the  sounding  body, 
provided  its  pitch  corresponds  exactly  with  the  pitch  of  one 
of  the  overtones  of  that  body. 

Thus,  if  the  damper  is  lifted  from  the  C  string  of  a  piano  and  the 
octave  below,  Cv  is  sounded  loudly,  C  will  be  heard  to  sound  after  C± 
has  been  quenched  by  the  damper.  In  this  case  it  is  the  first  overtone 
of  Cl  which  is  in  exact  tune  with  C,  and  which  therefore  sets  it  into 
sympathetic  vibration.  Again,  if  the  damper  is  lifted  from  the  G  string 
while  C\  is  sounded,  this  note  will  be  found  to  be  set  into  vibration  by 
the  second  overtone  of  Cr  A  still  more  interesting  case  is  obtained  by 
removing  the  damper  from  E  while  C1  is  sounded.  When  C1  is  quenched, 
the  note  which  is  heard  is  not  E,  but  an  octave  above  E ;  that  is,  £". 
This  is  because  there  is  no  overtone  of  Cl  which  corresponds  to  the  vi- 
bration of  E]  but  the  fourth  overtone  of  Cv  which  has  five  times  the 
vibration  number  of  Cv  corresponds  exactly  to  the  vibration  number  of 
E',  the  first  overtone  of  E.  Hence  E  is  set  into  vibration  not  as  a 
whole  but  in  halves. 

410.  Physical  significance  of  harmony  and  of  discord.  Let  two 
pieces  of  glass  tubing  about  an  inch  in  diameter  and  a  foot  and  a  half 
long  be  supported  vertically,  as  shown  in  Fig.  365.    Let  two  gas  jets 
(made  by  drawing  down  pieces  of  one-fourth  inch  glass  tubing  until,  with 
full  gas  pressure,  the  flame  is  about  an  inch  long)  be  thrust  inside  these 
tubes  to  a  height  of  about  three  or  four  inches  from  the  bottom.    Let 


348 


PEOPEETIES  OF  MUSICAL  SOUNDS 


the  gas  be  turned  down  until  the  tubes  begin  to  sing.  Without  attempt- 
ing to  discuss  the  part  which  the  flame  plays  in  the  production  of  the 
sound,  we  wish  simply  to  call  attention  to  the  fact  that  the  two  tones 
are  either  quite  in  unison  or  so  near  it  that  only  a 
few  beats  are  produced  per  second.  Now  let  the 
length  of  one  of  the  tubes  be  slightly  increased  by 
slipping  the  paper  cylinder  S  up  over  its  end.  The 
number  of  beats  will  be  rapidly  increased  until  they 
will  become  indistinguishable  as  separate  beats  and 
will  merge  into  a  jarring,  grating  discord. 

The  experiment  teaches  that  discord  is 
simply  a  phenomenon  of  beats.  If  the  vibra- 
tion numbers  do  not  differ  by  more  than 
five  or  six,  that  is,  if  there  are  not  more 
than  five  or  six  beats  per  second,  the  effect 
is  not  particularly  unpleasant.  From  this 
point  on,  however,  as  the  difference  in  the 
vibration  numbers,  and  therefore  in  the  num- 
ber of  beats  per  second,  increases,  the  un- 
pleasantness increases,  and  becomes  worst  at  FIG.  365.  Illustrat- 
a  difference  of  about  thirty.  Thus,  the  notes  ing  ^d?^f ion 
B  and  C",  which  differ  by  about  thirty-two 
beats  per  second,  produce  about  the  worst  possible  discord. 
When  the  vibration  numbers  differ  by  as  much  as  seventy, 
which  is  about  the  difference  between  C  and  E,  the  effect  is 
again  pleasing,  or  harmonious.  Moreover,  in  order  that  two 
notes  may  harmonize  well,  it  is  necessary  not  only  that  the 
notes  themselves  shall  not  produce  an  unpleasant  number 
of  beats,  but  also  that  such  beats  shall  not  arise  from  their 
overtones.  Thus,  C  and  B  are  very  discordant,  although  they 
differ  by  a  large  number  of  vibrations  per  second.  The  discord 
in  this  case  arises  between  B  and  C",  the  first  overtone  of  C. 

Again,  there  are  certain  classes  of  instruments,  of  which  bells 
are  a  striking  example,  which  produce  insufferable  discords 
when  even  such  notes  as  do,  sol,  do',  are  sounded  simultaneously 


WIND  INSTRUMENTS  349 

upon  them.  This  is  because  these  instruments,  unlike  strings 
and  pipes,  have  overtones  which  are  not  harmonics,  that  is, 
which  are  not  multiples  of  the  fundamental ;  and  these  over- 
tones produce  beats  either  among  themselves  or  with  one  of 
the  fundamentals.  It  is  for  this  reason  that  in  playing  chimes 
the  bells  are  struck  in  succession,  not  simultaneously. 

QUESTIONS  AND  PROBLEMS 

1.  In  what  three  ways  do  piano  makers  obtain  the  different  pitches? 

2.  What  did  Helniholtz  prove  by  means  of  his  resonators? 

3.  If  middle  C  is  struck  on  a  piano  while  the  key  for  G  in  the 
octave  above  is  held  down,  G  will  be  distinctly  heard  when  C  is  silenced. 
Explain. 

4.  At  what  point  must  the  G^  string  be  pressed  by  the  finger  of  the 
violinist  in  order  to  produce  the  note  C  ? 

5.  If  one  wire  has  twice  the  length  of  another  and  is  stretched 
by  four  times  the  stretching  force,  how  will  their  vibration  numbers 
compare  ? 

6.  A  wire  gives  out  the  note  G.   What  is  its  fourth  overtone? 

7.  If  middle  C  had  300  vibrations  per  second,  how  many  vibrations 
would  F  and  A  have  ? 

8.  What  is  the  fourth  overtone  of  C?  the  fifth  overtone? 

9.  There  are  seven  octaves  and  two  notes  on  an  ordinary  piano,  the 
lowest  note  being  A4  and  the  highest  one  C"".    If  the  vibration  number 
of  the  lowest  note  is  27,  find  the  vibration  number  of  the  highest. 

10.  Find  the  wave  length  of  the  lowest  note  on  the  piano;  the  wave 
length  of  the  highest  note.   (Take  the  speed  of  sound  as  1130  ft.  per  sec.) 

11.  A  violin  string  is  commonly  bowed  about  one  seventh   of  its 
length  from  one  end.    Why  is  this  better  than  bowing  in  the  middle  ? 

12.  Build  up  a  diatonic  scale  on  C  =  264. 

WIND  INSTRUMENTS 
411.  Fundamentals  of  closed  pipes.   Let  a  tightly  fitting  rubber 

stopper  be  inserted  in  a  glass  tube  a  (Fig.  366),  eight  or  ten  inches  long 
and  about  three  fourths  of  an  inch  in  diameter.  Let  the  stopper  be 
pushed  along  the  tube  until,  when  a  vibrating  C'  fork  is  held  before  the 
mouth,  resonance  is  obtained  as  in  §  391.  (The  length  will  be  six  or 
seven  inches.)  Then  let  the  fork  be  removed  and  a  stream  of  air  blown 


350 


PEOPEETIES  OF  MUSICAL  SOUNDS 


FIG.  366.  Musical  notes 
from  pipes 


across  the  mouth  of  the  tube  through  a  piece  of  tubing  b,  flattened  at 
one  end  as  in  the  figure.*  The  pipe  will  be  found  to  emit  strongly  the 
note  of  the  fork. 

In  every  case  it  is  found  that  a  note 
which  a  pipe  may  be  made  to  emit  is 
always  a  note  to  which  it  is  able  to  re- 
spond when  used  as  a  resonator.  Since, 
in  §  392,  the  best  resonance  was  found 
when  the  wave  length  given  out  by  the 
fork  was  four  times  the  length  of  the 
pipe,  we  learn  that  when  a  current  of  air 
is  suitably  directed  across  the  mouth  of  a 
closed  pipe,  it  will  emit  a  note  lohich  has  a 
wave  length  four  times  the  length  of  the 
pipe.  This  note  is  called  the  fundamental  of  the  pipe.  It 
is  the  lowest  note  which  the  pipe  can  be  made  to  produce. 

412.  Fundamentals  of  open  pipes.   Since  we  found  in  §  393 
that  the  lowest  note  to  which  a  pipe  open  at  the  lower  end 
can  respond  is  one  the  wave  length  of  which  is  twice  the  pipe 
length,  we  infer  that  an  open  pipe,  when  suitably  blown,  ought 
to  emit  a  note  the  wave  length  of  which  is  twice  the  pipe  length. 
This  means  that  if  the  same  pipe  is  blown  first  when  closed  at 
the  lower  end  and  then  when  open,  the  first  note  ought  to  be 
an  octave  lower  than  the  second. 

Let  the  pipe  a  (Fig.  366)  be  closed  at  the  bottom  with  the  hand  and 
blown  ;  then  let  the  hand  be  removed  and  the  operation  repeated.  The 
second  note  will  indeed  be  found  to  be  an  octave  higher  than  the  first. 

We  learn,  therefore,  that  the  fundamental  of  an  open  pipe 
has  a  wave  length  equal  to  twice  the  pipe  length. 

413.  Overtones  in  pipes.    It  was  found  in  §  392  that  there 
is  a  whole  series  of  pipe  lengths  which  respond  to  a  given 

*  If  the  arrangement  of  Fig.  366  is  not  at  hand,  simply  blow  with  the  lips 
across  the  edge  of  a  piece  of  ordinary  glass  tubing  within  which  a  rubber 
stopper  may  be  pushed  back  and  forth. 


WIND  INSTEUMENTS  351 

fork,  and  that  these  lengths  bear  to  the  wave  length  of  the 
fork  the  ratios  |,  |,  |,  etc.  This  is  equivalent  to  saying  that 
a  closed  pipe  of  fixed  length  can  respond  to  a  whole  series  of 
notes  whose  vibration  numbers  have  the  ratios  1,  3,  5,  7,  etc. 
Similarly,  in  §  393,  we  found  that  in  the  case  of  an  open  pipe 
the  series  of  pipe  lengths  which  will  respond  to  a  given  fork 
bear  to  the  wave  length  of  the  fork  the  ratios  J,  J,  |,  |-,  etc. 
This,  again,  is  equivalent  to  saying  that  an  open  pipe  can  re- 
spond to  a  series  of  notes  whose  vibration  numbers  have  the 
ratios  1,  2,  3,  4,  5,  etc.  Hence  we  infer  that  it  ought  to  be 
possible  to  cause  both  open  and  closed  pipes  to  emit  notes  of 
higher  pitch  than  their  fundamentals  (that  is,  overtones),  and 
that  the  first  overtone  of  an  open  pipe  should  have  twice  the 
rate  of  vibration  of  the  fundamental  (that  is,  it  should  be 
do',  the  fundamental  being  considered  as  do)  ;  that  the  second 
overtone  should  vibrate  three  times  as  fast  as  the  fundamental 
(that  is,  it  should  be  sol');  that  the  third  overtone  should 
vibrate  four  times  as  fast  (that  is,  it  should  be  do")  ;  that  the 
fourth  overtone  should  vibrate  five  times  as  fast  (that  is,  it 
should  be  mi") ;  etc.  In  the  case  of  the  closed  pipe,  however, 
the  first  overtone  should  have  a  vibration  rate  three  times 
that  of  the  fundamental  (that  is,  it  should  be  sol') ;  the 
second  overtone  should  vibrate  five  times  as  fast  (that  is,  it 
should  be  mi")  ;  etc.  In  other  words,  while  an  open  pipe 
ought  to  give  forth  all  the  harmonics,  both  odd  and  even,  a 
closed  pipe  ought  to  produce  the  odd  harmonics  but  be 
entirely  incapable  of  producing  the  even  ones. 

Let  the  pipe  of  Fig.  366  be  blown  so  as  to  produce  the  fundamental 
when  the  lower  end  is  open.  Then  let  the  strength  of  the  air  blast  be 
increased.  The  note  will  be  found  to  spring  to  do'.  By  blowing  still 
harder  it  will  spring  to  sol',  and  a  still  further  increase  will  probably 
bring  out  do".  The  odd  and  the  even  harmonics  are,  in  fact,  emitted 
by  the  open  pipe,  as  our  theory  predicted.  When  the  lower  end  is  closed, 
however,  the  first  overtone  will  be  found  to  be  sol',  and  the  next  one  mi", 
just  as  our  theory  demands  for  the  closed  pipe. 


352  PKOPERTIES  OF  MUSICAL  SOUNDS 

414.  Mechanism  of  emission  of  notes  by  pipes.  Blowing 
across  the  mouth  of  a  pipe  produces  a  musical  note,  because 
the  jet  of  air  vibrates  back  and  forth  across  the  lip  in  a 
period  which  is  determined  wholly  by  the  natural  resonance 
period  of  the  pipe.  Thus,  suppose  that  the  jet  a  (Fig.  367) 
first  strikes  just  inside  the  edge,  or  Up,  of  the  pipe.  A  con- 
densational pulse  starts  down  the  pipe.  When  it  returns  to 
the  mouth  after  reflection  at  the  closed  end,  it  pushes  the  jet 
outside  the  lip.  This  starts  a  rarefaction  down  the  pipe,  which, 
after  return  from  the  lower  end,  pulls  the  jet  in  again. 
There  are  thus  sent  out  into  the  room  regu- 
larly timed  puffs,  the  period  of  which  is  con- 
trolled by  the  reflected  pulses  coming  back 
from  the  lower  end,  that  is,  by  the  natural 
resonance  period  of  the  pipe. 

By  blowing  more  violently  it  is  possible 
to  create,  by  virtue  of  the  friction  of  the 
walls,  so  great  and  so  sudden  a  compression 
in  the  mouth  of  the  pipe  that  the  jet  is  forced  FlG:  367\  vibrat- 
out  over  the  edge  before  the  return  of  the 
first  reflected  pulse.  In  this  case  no  note  will  be  produced 
unless  the  blowing  is  of  just  the  right  intensity  to  cause  the 
jet  to  swing  out  in  the  period  corresponding  to  an  overtone. 
In  this  case  the  reflected  pulses  will  return  from  the  end  at 
just  the  right  intervals  to  keep  the  jet  swinging  in  this 
period.  This  shows  why  a  current  of  a  particular  intensity 
is  required  to  start  any  particular  overtone. 

Another  way  of  looking  at  the  matter  is  to  think  of  the 
pipe  as  being  filled  up  with  air  until  the  pressure  within  it  is 
great  enough  to  force  the  jet  outside  the  lip,  upon  which  a 
period  of  discharge  follows,  to  be  succeeded  in  turn  by 
another  period  of  charge.  These  periods  are  controlled  by 
the  length  of  the  pipe  and  the  violence  of  the  blowing, 
precisely  as  described  above. 


WIND  INSTRUMENTS 


353 


0 

jm 
If 

( 

I        U 

FIG.  368.    Organ 
pipes 

With  open  pipes  the  situation  is  in  no  way  different  save 
that  the  reflection  of  a  condensation  as  a  rarefaction  at  the 
lower  end  makes  the  natural  period  twice  as 
high,  since  the  pipe  length  is  now  one-half 
wave  length  instead  of  one-fourth  wave 
length  (see  §  393). 

415.  Vibrating  air-jet  instruments.  The  mechanism 
of  the  production  of  musical  tones  by  the  ordinary 
organ  pipe,  the  flute,  the  fife,  the 
piccolo,  and  all  whistles  is  essen- 
tially the  same  as  in  the  case  of 
the  pipe  of  Fig.  367.  In  all  these 
instruments  an  air  jet  is  made  to 
play  across  the  edge  of  an  opening 
in  an  air  chamber,  and  the  reflected 
pulses  returning  from  the  other 
end  of  the  chamber  cause  it  to 
vibrate  back  and  forth,  first  into 

the  chamber  and  then  out  again. 
FIG.  369.  Moutt 

net,  showing  the 
ton  ue  I  which 
opens  and  closes 

the  upper  end  of     closed  at  the  remote  end.    In  the  flute  it  is  open,  in 
the  pipe  whistles  it  is  usually  closed,  and  in  organ  pipes  it 

may  be  either  open  or  closed.  Fig.  368  shows  a  cross 
section  of  two  types  of  organ  pipes.  The  jet  of  air  from  S  vibrates 
across  the  lip  L  in  obedience  to  the  pressure  exerted  on  it  by  waves 
reflected  from  O.  Pipe  organs  are  provided  with  a  different  pipe  for 
each  note,  but  the  flute,  piccolo, 
and  fife  are  made  to  produce  a 
whole  series  of  notes,  either  by 
blowing  overtones  or  by  open- 
ing holes  in  the  tube,  —  an  oper- 
ation which  is  equivalent  to 
cutting  the  tube  off  at  the  hole. 
Although  important  orchestral 
instruments,  the  flute  and  pic-  FIG.  370.  The  vibrating  tongue  of  the 
colo  are  not  rich  in  overtones.  mouth  organ,  accordion,  etc. 


of  regularly  timed  puffg  of  air  ig 
made  to  pass  from  the  instrument  to  the  ear  of  the 
observer  precisely  as  in  the  case  of  the  rotating  disk 
air  chamber  may  be  either  open  or 


354  PKOPERTIES  OF  MUSICAL  SOUNDS 

416.  Vibrating    reed    instruments.    In  reed  instruments  the  vibrating 
air  jet  is  replaced  by  a  vibrating  reed,  or  tongue,  which  opens  and  closes, 
at  absolutely  regular  intervals,  an  opening  against  which 

the  performer  is  directing  a  current  of  air.  In  the  clari- 
net, the  oboe,  the  bassoon,  etc.  the  reed  is  placed  at  the 
upper  end  of  the  tube  (see  /,  Fig.  369),  and  the  theory 
of  its  opening  and  closing  the  orifice  so  as  to  admit 
successive  puffs  of  air  to  the  pipe  is  identical  with  the 
theory  of  the  fluctuation  of  the  air  jet  into  and  out  of 
the  organ  pipe.  For  in  these  instruments  the  reed  has 
little  rigidity  and  its  vibrations  are  controlled  largely 
by  the  reflected  pulses  but  partly  by  the  reed  and  by 
the  lips  of  the  performer. 

In  other  reed  instruments,  like  the  mouth  organ,  the 
common  reed  organ,  or  the  accordion,  it  is  the  elasticity 
of  the  reed  alone  (see  z,  Fig.  370)  which  controls  the 
emission  of  pulses.  In  such  instruments  there  is  no 
necessity  for  air  chambers.  The  arrows  of  Fig.  370  in- 
dicate the  direction  of  the  air  current  which  is  inter- 
rupted as  the  reed  vibrates  between  the  positions  z±  ^  ^-j  T, 

an     *2  reed-organ  pipe 

In  still  other   reed  instruments,  like  the  reed  pipes 

used  in  large  organs  (Fig.  371),  the  period  of  the  pulses  is  controlled 
partly  by  the  elasticity  of  the  reed  and  partly  by  the  return  of  the 
reflected  waves ;  in  other  words,  the  natural  period  of  the  reed  is  more 
or  less  coerced  by  the  period  of  the  reflected  pulses.  Within  certain 
limits,  therefore,  such  in- 
struments may  be  tuned  by 
changing  the  length  of  the 
vibrating  reed  /  without 
changing  the  length  of  the 
pipe.  This  is  done  by  push- 
ing the  wire  r  up  or  down. 

417.  Vibrating    lip    in- 
struments.   In  instruments 

of    the  bugle    and    cornet  -pio.  372.   The  cornet 

type  the  vibrating  reed  is 

replaced  by  the  vibrating  lips  of  the  musician,  the  period  of  their  vibra- 
tion being  controlled,  precisely  as  in  the  organ  pipe  or  the  clarinet,  by 
the  period  of  the  returning  pulses.  In  the  bugle  the  pipe  length  is  fixed, 


WIND  INSTRUMENTS 


355 


FIG.  373 


I  Cover 


and  because  of  the  narrowness  of  the  tube  all  bugle  calls  are  played  with 

overtones.  In  the  cornet  (Fig.  372)  and  in  most  forms  of  horns,  valves 
o,  />,  c,  worked  by  the  fingers,  vary  the  length  of  the 
pipe,  and  hence  such  instruments  can  produce  as 
many  series  of  fundamentals  and  overtones  as  there 
are  possible  tube  lengths.  In  the  trombone  the 
variation  of  pitch  is 
accomplished  by  blow- 
ing overtones  and  by 

changing  the  length  of   the  tube  by  a 

sliding  U-shaped  portion 

418.  The  phonograph.   In  the  original 

form  of  the  phonograph  the  sound  waves, 

collected  by  the  cone,  are  carried  to  a 

thin  metallic  disk  C  (Fig.  373),  exactly 

like  a  telephone  diaphragm,  which  takes 

up  very  nearly  the  vibration  form  of  the 

wave  which  strikes  it.     This   vibration 

form  is  permanently  impressed  on  the 

wrax-coated  cylinder  M  by  means  of  a 

stylus  D  which  is  attached  to  the  back 


Glass 
Diaphragm 

C 


\Needle  Point 
\D 

FIG.  374.  Mechanism  for  form- 
ing gramophone  records 


of  the  disk.  When  the  stylus  is  run  a  second  time  over  the  groove  which 
it  first  made  in  the  wax,  it  receives  again  and  imparts  to  the  disk  the 
vibration  form  which  first  fell  upon  it.  This  is  the  principle  of  the 


Vegetable- 
Tissue 
Diaphragm 


The  diamond  point 

FIG.  375.    The  Edison  diamond  reproducer 


356  PROPERTIES  OF  MUSICAL  SOUNDS 

dictaphone  and  the  ediphone,  used  to  replace  stenographers  in  business 
offices.  The  typist  writes  the  letter  by  listening  to  the  reproduction 
of  the  dictation. 

In  the  most  familiar  of  the  modern  forms  of  the  phonograph  (gramo- 
phone, etc.)  the  needle  point  D,  instead  of  digging  a  groove  in  wax, 
vibrates  back  and  forth  (see  Fig.  374)  over  a  greased  zinc  disk.  This 
wavy  trace  in  the  disk  is  etched  out  with  chromic  acid.  Then  a  copper 
mold  is  made  by  the  electeotyping  process,  and  as  many  as  a  thousand 
facsimiles  of  the  original  wavy  line  are  impressed  on  hard-rubber  disks 
by  heat  and  pressure.  When  the  needle  is  again  run  over  the  disk,  it 
follows  along  the  wavy  groove  and  transmits  to  the  diaphragm  C  vibra- 
tions exactly  like  those  which  originally  fell  upon  it.  Spoken  words 
and  vocal  and  orchestral  music  are  reproduced  in  pitch,  loudness,  and 
quality  with  wonderful  exactness.  This  instrument  is  one  of  the  many 
inventions  of  Thomas  Edison  (see  opposite  p.  316).  The  diamond-tip 
reproducer  used  with  the  hill-and-dale  Edison  disks  is  shown  in  Fig.  375. 

QUESTIONS  AND  PROBLEMS 

1.  What  proves  that  a  musical  note  is  transmitted  as  a  wave  motion  ? 

2.  What  evidence  have  you  that  sound  waves  are  longitudinal 
vibrations  ? 

3.  Why  is  the  pitch  of  a  sound  emitted  by  a  phonograph  raised  by 
increasing  the  speed  of  rotation  of  the  disk  ? 

4.  AVhat  will  be  the  relative  lengths  of  a  series  of  organ  pipes  which 
produce  the  eight  notes  of  a  diatonic  scale  ? 

5.  Will  the  pitch  of  a  pipe  organ  be  the  same  in  summer  as  on 
a  cold  day  in  winter?    What  could  cause  a  difference? 

6.  Explain  how  an  instrument  like  the  bugle,  which  has  an  air 
column  of  unchanging  length,  may  be  made  to  produce  several  notes 
of  different  pitch,  such  as  C,  G,  C\  E',  G'.    (C  is  not  often  used.) 

7.  Why  is  the  quality  of  an  open  organ  pipe  different  from  that 
of  a  closed  organ  pipe  ? 

8.  The  velocity  of  sound  in  hydrogen  is  about  four  times  as  great 
as  it  is  in  air.    If  a  C  pipe  is  blown  with  hydrogen,  what  will  be  the 
pitch  of  the  note  emitted  ? 

9.  What  effect  will  be  produced  on  a  phonograph  record  made  with 
the  instrument  of  Fig.  374  if  the  loudness  of  a  note  is  increased?   if 
the  pitch  is  lowered  an  octave? 


CHAPTER  XVIII 


NATURE  AND  PROPAGATION  OF  LIGHT 

TRANSMISSION  OF  LIGHT 

419.  Speed  of  light.  Before  the  year  1675  light  was  thought 
to  pass  instantaneously  from  the  source  to  the  observer.  In 
that  year,  however,  Olaus  Romer,  a  young  Danish  astron- 
omer, made  the  following  observations.  He  had  observed 
accurately  the  instant  at  which  one  of  Jupiter's  satellites  M 
(Fig.  376)  passed  into 

Jupiter's  shadow  when  1C 

the  earth  was  at  E, 
and  predicted,  from  the 
known  mean  time  be- 
tween such  eclipses,  the 
exact  instant  at  which 
a  given  eclipse  should 
occur  six  months  later 
when  the  earth  was 
at  E'.  It  actually  took 
place  16  minutes  36 
seconds  (996  seconds)  later.  He  concluded  that  the  996 
seconds'  delay  represented  the  time  required  for  light  to 
travel  across  the  earth's  orbit,  a  distance  known  to  be  about 
180,000,000  miles.  The  most  precise  of  modern  determinations 
of  the  speed  of  light  are  made  by  laboratory  methods.  The 
generally  accepted  value,  that  of  Michelson,  of  The  University 
of  Chicago,  is  299,860  kilometers  per  second.  It  is  sufficiently 
correct  to  remember  it  as  300,000  kilometers,  or  186,000  miles. 

357 


FIG.  376.    Illustrating  Romer's  determination 
of  the  velocity  of  light 


358       NATURE  AND  PROPAGATION  OF  LIGHT 


Though  this  speed  would  carry  light  around  the  earth  1\  times 
in  a  second,  yet  it  is  so  small  in  comparison  with  interstellar 
distances  that  the  light  which  is  now  reaching  the  earth  from 
the  nearest  fixed  star,  Alpha  Centauri,  started  4.4  years 
ago.  If  an  observer  on  the  pole  star  had  a  telescope  powerful 
enough  to  enable  him  to  see  events  on  the  earth,  he  would 
not  have  seen  the  battle  of  Gettysburg  (which  occurred  in 
July,  1863)  until  January,  1918. 

Both  Foucault  in  France  and  Michelson  in  America  have 
measured  directly  the  velocity  of  light  in  water  and  have 
found  it  to  be  only  three  fourths  as  great  as  in  air.  It  will 
be  shown  later  that  in  all  transparent  liquids  and  solids  it 
is  less  than  it  is  in  air. 

420.  Reflection  Of  light.*  Let  a  beam  of  sunlight  be  admitted  to 
a  darkened  room  through  a  narrow  slit.  The  straight  path  of  the  beam 
will  be  rendered  visible  by  the  brightly  illumined  dust  particles  sus- 
pended in  the  air.  Let  the  beam  fall  on  the  surface  of  a  mirror.  Its 
direction  will  be  seen  to  be  sharply 
changed,  as  shown  in  Fig.  377.  Let 
the  mirror  be  held  so  that  it  is  per- 
pendicular to  the  beam.  The  beam  will 
be  seen  to  be  reflected  directly  back 
on  itself.  Let  the  mirror  be  turned 
through  an  angle  of  45°.  The  reflected 
beam  will  move  through  90°. 


FIG.  377.    Illustrating  law  of 
reflection  of  light 


The  experiment  shows  roughly, 
therefore,  that  the  angle  IOP,  be- 
tween the  incident  beam  and  the 

normal  to  the  mirror,  is  equal  to  the  angle  FOR,  between  the  re- 
flected beam  and  the  normal  to  the  mirror.  The  first  angle,  IOP, 
is  called  the  angle  of  incidence,  and  the  second,  FOR,  the  angle  of 
reflection.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

*  An  exact  laboratory  experiment  on  the  law  of  reflection  should  either 
precede  or  follow  this  discussion.  See,  for  example,  Experiment  42  of  the 
authors'  Manual. 


A.  A.  MICHELSON,  CHICAGO 

Distinguished  for  extraordinarily  accu- 
rate experimental  researches  in  light. 
First  American  scientist  to  receive  the 
Nobel  prize 


LOUD  RAYLEIGH  (ENGLAND) 

Distinguished  for  the  discovery  of  argon , 
for  very  accurate  determinations  in  elec- 
tricity and  sound  and  for  profound  theo- 
retical studies 


HENRY  A.  ROWLAND,  JOHNS  HOPKINS 

Distinguished  for  the  invention  of  the 

concave  grating  and  for  epoch-making 

studies  in  heat  and  electricity 


SIB  WILLIAM  CROOKES,  LONDON 

Distinguished  for  his  pioneer  work  (1875) 
in  the  study  and  interpretation  of  cath- 
ode rays  (pp.438  and  443) 


A  GROUP  OF  MODERN  PHYSICISTS 


X-RAY   PICTURE  OF  THE  HUMAN  THORAX 

This  figure  is  a  remarkable  picture  of  the  human  thorax  with  the  apex  of  the 
heart  showing  clearly  on  the  right  of  the  spinal  column  and  the  base  stretching 
across  the  column,  part  of  it  showing  distinctly  on  the  left  side  opposite  the  apex 


TRANSMISSION  OF  LIGHT  359 

421.  Diffusion  of  light.    In  the  last  experiment  the  light  was 
reflected  by  a  very  smooth  plane  surface.    Now  let  the  beam  be  allowed 
to  fall  upon  a  rough  surface  like  that  of  a  sheet  of  unglazed  white  paper. 
No  reflected  beam  will  be  seen;  but  instead  the  whole  room  will  be 
brightened  appreciably,  so  that  the  outline  of  objects  before  invisible 
may  be  plainly  distinguished. 

The  beam  has  evidently  been  scattered  in  all  directions  by 
the  innumerable  little  reflecting  surfaces  of  which  the  surface 
of  the  paper  is  composed.  The  effect  will  be'  much  more 
noticeable  if  the 
beam  is  allowed 
to  fall  alternately 
on  a  piece  of  dead- 
black  cloth  and  on 

FIG.  378.    Regular  and  irregular  reflection 
the  white  paper. 

The  light  is  largely  absorbed  by  the  cloth,  while  it  is  scattered 
or  diffusely  reflected  by  the  paper.  Illumination  sufficiently 
strong  for  sewing  on  white  material  may  be  altogether  too 
weak  for  working  on  black  goods.  The  difference  between 
a  smooth  reflector  and  a  rough  one  is  illustrated  in  greatly 
magnified  form  in  Fig.  378.  The  air  shafts  of  apartment 
houses  are  made  white  to  get  the  maximum  diffusion  of  day- 
light into  rooms  that  might  otherwise  be  very  dark. 

422.  Visibility  of  nonluminous  bodies.    Everyone  is  familiar 
with  the  fact  that  certain  classes  of  bodies,  such  as  the  sun,  a 
gas  flame,  etc.,  are  self-luminous  (that  is,  visible  on  their  own 
account),  while  other  bodies,  like  books,  chairs,  tables,  etc.,  can 
be  seen  only  when  they  are  in  the  presence  of  luminous  bodies. 
The  above  experiment  shows  how  such  nonluminous,  diffusing 
bodies  become  visible  in  the  presence  of  luminous  bodies.   For, 
since  a  diffusing  surface  scatters  in  all  directions  the  light 
which  falls  upon  it,  each  small  element  of  such  a  surface  is 
sending  out  light  in  a  great  many  directions,  in  much  the 
same  way  in  which  each  point  on  a  luminous  surface  is  sending 


860        NATUKE  AND  PROPAGATION  OF  LIGHT 


out  light  in  all  directions.  Hence  we  always  see  the  outline 
of  a  diffusing  surface  as  we  do  that  of  an  emitting  surface, 
no  matter  where  the  eye  is  placed.  On  the  other  hand,  when 
light  comes  to  the  eye  from  a  polished  reflecting  surface,  since 
the  form  of  the  beam  is  wholly  undisturbed  by  the  reflection, 
we  see  the  outline  not  of  the  mirror  but  rather  of  the  source 
from  which  the  light  came  to  the  mirror,  whether  this  source 
is  itself  self-luminous  or  not.  All  bodies  other  than  self- 
luminous  ones  are  visible  only  by  the  light  which  they  diffuse. 
Black  bodies  send  no  light  to  the  eye,  but  their  outlines  can 
be  distinguished  by  the  light  which  comes  from  the  back- 
ground. Any  object  which  can  be  seen,  therefore,  may  be  re- 
garded as  itself  sending  rays  to  the  eye ;  that  is,  it  may  be 
treated  as  a  luminous  body. 

423.  Refraction.  Let  a  narrow  beam  of  sunlight  be  allowed  to  fall 
on  a  thick  glass  plate  with  a  polished  front  and  whitened  back*  (Fig.  379). 
It  will  be  seen  to  split  into  a  re- 
flected and  a  transmitted  portion. 
The  transmitted  portion  will  be 
seen  to  be  bent  toward  the  per- 
pendicular OP  drawn  into  the 
glass.  Upon  emergence  into  the 
air  it  will  be  bent  again,  but 
this  time  away  from  the  per- 
pendicular O'P'  drawn  into  the 
air.  Let  the  incident  beam  strike 


FIG.  379.   Path  of  a  ray  through  a 
medium  bounded  by  parallel  faces 


the  surface  at  different  angles. 

It  will  be  seen  that  the  greater  the 

angle  of  incidence  the  greater  the 

bending.    At  normal  incidence  there  will  be  no  bending  at  all.    If  the 

upper  and  lower  faces  of  the  glass  are  parallel,  the  bending  at  the  two 

faces  will  always  be  the  same,  so  that  the  emergent  beam  is  parallel 

to  the  incident  beam. 

*A11  of  these  experiments  on  reflection  and  refraction  may  be  done 
effectively  and  conveniently  by  using  disks  of  glass,  like  those  used  with  the 
Hart!  Optical  Disk,  through  which  the  beam  can  be  traced. 


TRANSMISSION  OF  LIGHT 


361 


Similar  experiments  made  with  other  substances  have 
brought  out  the  general  law  that  whenever  light  travels  obliquely 
from  one  medium  into  another  in  which  the  speed  is  less  it  is  lent 
toivard  the  perpendicular,  and  when  itfia&sesfrom  one  medium  to 
another  in  which  the  speed  is  greater 
it  is  bent  away  from  the  perpendic- 
ular, drawn  into  the  second  medium. 

424.  Total  reflection ;  critical 
angle.  Since  rays  emerging  from 
a  medium  like  water  into  one  of 
less  density,  like  air,  are  always 
bent /row  the  perpendicular  (see 
II A,  ImB,  etc.,  Fig.  380),  it  is  clear 
that  if  the  angle  of  incidence  on 
the  under  surface  of  the  water  is 
made  larger  and  larger,  a  point  must  be  reached  at  which  the 
refracted  ray  is  parallel  to  the  surface  (see  InC,  Fig.  380).  It 
is  interesting  to  inquire  what  will  happen  to  a  ray  lo  which 
strikes  the  surface  at  a  still  greater  angle  of  incidence  IoPf. 
It  will  not  be  unnatural  to  suppose  that  since  the  ray  nC  just 
grazed  the  surface,  the  ray  lo  will 
not  be  able  to  emerge  at  all.  The 

O 

following  experiment  will  show  that 
this  is  indeed  the  case. 


FIG.  380.  Rays  coming  from  a 
source  I  under  water  to  the 
boundary  between  air  and  water 
at  different  angles  of  incidence 


Let  a  prism  with  three  polished  edges, 
a  polished  front,  and  a  whitened  back  be 
held  in  the  path  of  a  narrow  beam  of  sun- 
light,1 as  shown  in  Fig.  381.  If  the  angle 
of  incidence  I  OP  is  small,  the  beam  will 
divide  at  0  into  a  reflected  and  a  trans- 
mitted portion,  the  former  going  to  5', 
the  latter  to  S  (neglect  the  color  for  the  present).  Let  the  prism  be 
rotated  slowly  in  the  direction  of  the  arrow.  A  point  will  be  reached  at 
which  the  transmitted  beam  disappears  completely,  while  at  the  same 
time  the  spot  at  S'  shows  an  appreciable  increase  in  brightness.  Since 


FIG.  381.  Transmission  and 
reflection  of  light  at  surface 
AB  of  a  right-angled  prism 


362       NATURE  AND  PROPAGATION  OF  LIGHT 

the  transmitted  ray  OS  has  totally  disappeared,  the  whole  of  the  light 
incident  at  O  must  be  in  the  reflected  beam.  The  angle  of  incidence 
IOP  at  which  this  occurs  is  called  the  critical  angle.  This  angle  for 
crown  glass  is  42.5°,  for  water  48.5°,  for  diamond  23.7°.  The  critical 
angle  for  any  substance  may  be  defined  as  the  angle  of  incidence  in 
that  substance  for  which  the  angle  of  refraction  into  air  is  90°. 

We  learn,  then,  that  when  a  ray  of  light  traveling  in  any 
medium  meets  another  in  which  the  speed  is  greater,  it  is  totally 
reflected  if  the  angle  of  incidence  is  greater  than  a  certain  angle 
called  the  critical  angle. 


QUESTIONS  AND  PROBLEMS 

1.  In  Fig.  382  the  portion  acdb  of  the  shadow  is  called  the  umbra, 
aec  and  Idf  the  penumbra.    What  kind  of  source  has  no  penumbra  ? 

2.  The  sun  is  much  larger  than  the  earth.    Draw 
a  diagram  showing  the  shape  of  the  earth's  umbra 
and  penumbra. 

3.  Will  it  ever  be  possible  for  the  moon  to  totally 
eclipse  the  sun  from  the 

whole   of  the  earth's  sur- 
face at  once  ? 

4.  Sirius,  the  brightest 
star,  is  about  52,000,000,- 
000,000  miles  away.  If  it 
were  suddenly  annihilated, 
how  long  would  it  shine  on 
for  us  ? 

5.  Why  is  a  room  with      JT  FlG-  383'     Anti~ 

glare  "  lens  "  for 

EIG.  382.    Shadow  from      automobile  head- 
a  broad  source  light 


white  walls  much  lighter 
than  a  similar  room  with 
black  walls  ? 

6.  If  the  word  "  white  : 


be  painted  with  white  paint  (or  whiting 
moistened  with  alcohol)  across  the  face  of  a  mirror  and  held  in  the  path 
of  a  beam  of  sunlight  in  a  darkened  room,  in  the  middle  of  the  spot  on 
the  wall  which  receives  the  reflected  beam  the  word  "  white  "  will  appear 
in  black  letters.  Explain. 

7.  Compare  the  reflection  of  light  from  white  blotting  paper  with, 
that  from  a  plane  mirror.  Which  of  these  objects  is  more  easily  seent 
from  a  distance  ?  Why  ? 


TRANSMISSION  OF  LIGHT 


363 


8.  Devise  an  arrangement  of  mirrors  by  means  of  which  you  could 
see  over  and  beyond  a  high  stone  wall  or  trench  embankment.    This  is 
a  very  simple  form  of  periscope. 

9.  Draw  diagrams  to  show  in  what  way  a  beam  of  light  is  bent 
(a)  in  passing  through  a  prism;  (b)  in  passing  obliquely  through  a 
plate-glass  window. 

10.  Explain  the  effect  of  the  anti-glare 
"  lens "   (Fig.  383)  upon  the  light  of  the 
automobile. 

11.  The  moon  has  practically  no  atmos- 
phere. We  know  this  because  when  a  star 

appears  to  pass  behind  the  moon  there  is  FIG.  384 

no    decrease   or   increase  in   its  apparent 

velocity  while  disappearing  or  coming  into  view  again.    If  the  moon 

had  an  atmosphere  like  the  earth,  explain  how  this  would  affect  the 

apparent  velocity  of  the  star  at  both  these  times. 

12.  If  a  penny  is  placed  in  the  bottom  of  a  vessel  in  such  a  position 
that  the  edge  just  hides  it  from  view  (Fig.  384),  it  will  become  visible  as 
soon  as  water  is  poured  into  the  vessel.    Explain. 


FIG.  385 


FIG.  386 


FIG.  387.   A  diagonal 
eyepiece 


13.  A  stick  held  in  water  appears  bent,  as  shown  in  Fig.  385.  Explain. 

14.  A  glass  prism  placed  in  the  position  shown  in  Fig.  386  is  the 
most  perfect  reflector  known.    Why  is  it  better  than  an 
ordinary  mirror? 

15.  Diagonal  eyepieces  containing  a  right-angle  prism  of 
crown  glass  (Fig.  387)  are  used  on  astronomical  telescopes 
in  viewing  celestial  objects  at  a  high  altitude.    Explain. 

16.  Explain  why  a  straight  wire  seen  obliquely  through 
a  piece  of  glass  appears  broken,  as  in  Fig.  388. 

17.  The  earth  reflects  sixteen  times  as  much  light  to  the  moon  as 
the  moon  does  to  the  earth.  Trace  from  the  sun  to  the  eye  of  the  ob- 
server the  light  by  which  he  is  able  to  see  the  dark  part  of  the  new 
moon.    Why  can  we  not  see  the  dark  part  of  a  third-quarter  moon? 


FIG.  388 


364       NATUKE  AND  PKOPAGATION  OF  LIGHT 

THE  NATURE  OF  LIGHT 

425.  The  corpuscular  theory  of  light.    All  of  the  properties 
of  light  which  have  so  far  been  discussed  are  perhaps  most 
easily  accounted  for  on  the  hypothesis  that  light  consists  of 
streams  of  very  minute  particles,  or  corpuscles,  projected  with 
the  enormous  velocity  of  300,000  kilometers  per  second  from 
all  luminous  bodies.     The  facts  of  straight-line  propagation 
and  reflection  are  exactly  as  we  should  expect  them  to  be  if 
this  were  the  nature  of  light.   The  facts  of  refraction  can  also 
be   accounted  for,   although  somewhat  less  simply,  on  this 
hypothesis.    As  a  matter  of  fact,  this  theory  of  the  nature  of 
light,  known   as   the   corpuscular   theory,  was   the  one   most 
generally  accepted  up  to  about  1800. 

426.  The  wave  theory  of  light.    A  rival  hypothesis,  which 
was  first  completely  formulated  by  the  great  Dutch  physicist 
Huygens  (1629-1695),  regarded  light,  like  sound,  as  &  form 
of  wave  motion.     This  hypothesis  met  at  the  start  with  two 
very   serious   difficulties.      In   the   first  place,   light,   unlike 
sound,  not  only  travels  with  perfect  readiness  through  the 
best  vacuum  which  can  be  obtained  with  an  air  pump,  but 
it  travels  without  any  apparent  difficulty  through  the  great 
interstellar  spaces  which  are  probably  infinitely  better  vacua 
than  can  be  obtained  by  artificial  means.    If,  therefore,  light 
is  a  wave  motion,  it  must  be  a  wave  motion  of  some  medium 
which  fills  all  space  and  yet  does  not  hinder  the  motion  of  the 
stars  and  planets.    Huygens  assumed  such  a  medium  to  exist, 
and  called  it  the  ether. 

The  second  difficulty  in  the  way  of  the  wave  theory  of 
light  was  that  it  apparently  failed  to  account  for  the  fact  of 
straight-line  propagation.  Sound  waves,  water  waves,  and 
all  other  forms  of  waves  with  which  we  are  most  familiar 
bend  readily  around  corners,  while  light  apparently  does  not. 
It  was  this  difficulty  chiefly  which  led  many  of  the  most 


CHRISTIAN  HUYGENS  (1629-1695) 

Great  Dutch  physicist,  mathematician,  and  astronomer;  dis- 
covered the  rings  of  Saturn ;  made  important  improvements  in 
the  telescope ;  invented  the  pendulum  clock  (1656) ;  developed 
with  marvelous  insight  the  wave  theory  of  light;  discovered  in 
1690  the  "polarization  "  of  light.  (The  fact  of  double  refraction 
was  discovered  by  Erasmus  Bartholinus  in  1669,  but  Huygens 
first  noticed  the  polarization  of  the  doubly  refracted  beams  and 
offered  an  explanation  of  double  refraction  from  the  standpoint 
of  the  wave  theory) 


THE  GREAT  TELESCOPE  OF  THE  YERKES  OBSERVATORY  (UNIVERSITY 
OF  CHICAGO) 

This  is  the  largest  refracting  telescope  in  the  world.  The  objective  is  an  achro- 
matic lens  (see  §  475)  40  inches  in  diameter,  which  is  mounted  in  a  tube  63  feet 
long.  In  order  to  follow  the  apparent  motions  of  the  heavenly  bodies  due  to  the 
rotation  of  the  earth,  the  entire  tube  and  counterpoises,  weighing  21  tons,  are 
driven  by  a  giant  clock.  The  speed  of  the  clock  is  controlled  by  a  governor, 
similar  in  principle  to  that  of  Fig.  184.  By  means  of  electric  motors  the  telescope 
may  be  pointed  in  any  direction.  It  fs  then  clamped  to  the  clock,  which  keeps  it 
pointed  toward  the  same  region  of  the  sky  as  long  as  may  be  desired.  The  entire 
floor  may  be  raised  or  lowered  to  accommodate  the  observer 


THE  NATURE  OF  LIGHT 


365 


famous  of  the  early  philosophers,  including  the  great  Sir 
Isaac  Newton,  to  reject  the  wave  theory  and  to  support  the 
projected-particle  theory.  Within  the  last  hundred  years, 
however,  this  difficulty  has  been  completely  removed,  and 
in  addition  other  properties  of  light  have  been  discovered 
for  which  the  wave  theory  offers  the  only  satisfactory  expla- 
nation. The  most  important  of  these  properties  will  be  treated 
in  the  next  paragraph. 

427.  Interference  Of  light.  Let  two  pieces  of  plate  glass  about 
half  an  inch  wide  and  four  or  five  inches  long  be  separated  at  one  end 
by  a  thin  sheet  of  paper  in  the  manner  shown  in  Fig.  389,  while  the 
other  end  is  clamped  or  held  firmly  together,  so  that  a  very  thin  wedge 
of  air  exists  between  the  plates.  Let  a  piece 
of  asbestos  or  blotting  paper  be  soaked  in 
a  solution  of  common  salt  (sodium  chlo- 
ride) and  placed  over  the  tube  of  a  Bunsen 
burner  so  as  to  touch  the  flame  in  the 
manner  shown.  The  flame  will  be  colored 
a  bright  yellow  by  the  sodium  in  the  salt. 
When  the  eye  looks  at  the  reflection  of 
the  flame  from  the  glass  surfaces,  a  series 
of  fine  black  and  yellow  lines  will  be  seen 
to  cross  the  plate. 


Paper 


FIG.  389.    Interference  of 
light  waves 


The  wave  theory  offers  the  fol- 
lowing explanation  of  these  effects. 
Each  point  of  the  flame  sends  out 
light  waves  which  travel  to  the  glass 
plate  and  are  in  part  reflected  and  in 

part  transmitted  at  all  the  surfaces  of  the  glass,  that  is,  at  A'Bry 
at  AB,  at  CD,  and  at  C'D'  (Fig.  389).  We  will  consider,  how- 
ever, only  those  reflections  which  take  place  at  the  two  faces 
of  the  air  wedge,  namely,  at  AB  and  CD.  Let  Fig.  390  repre- 
sent a  greatly  magnified  section  of  these  two  surfaces.  Let 
the  wavy  line  as  represent  a  light  wave  reflected  from  the 
surface  AB  at  the  point  a,  and  returning  thence  to  the  eye.- 


366        NATURE  AND  PROPAGATION  OF  LIGHT 


CA 


Let  the  dotted  wavy  line  ir  represent  a  light  wave  reflected 
from  the  surface  CD  at  the  point  i,  and  returning  thence  to 
the  eye.  Similarly,  let  all  the  continuous  wavy  lines  of  the 
figure  represent  light  waves  reflected  from  different  points  on 
AB  to  the  eye,  and  let  all  the  dotted  wavy  lines  represent 
waves  reflected  from  corresponding  points  on  CD  to  the  eye. 
Now,  in  precisely  the  same  way  in  which  two  trains  of  sound 
waves  from  two  tun- 
ing forks  were  found, 
in  the  experiment  il- 
lustrating beats  (see 
§  396),  to  interfere 
with  each  other  so  as 
to  produce  silence 
whenever  the  two 
waves  corresponded 
to  motions  of  the  air 
particles  in  opposite 
directions,  so  in  this 
experiment  the  two 
sets  of  light  waves 
from  A B  and  CD  inter- 
fere with  each  other 
so  as  to  produce  darkness  wherever  these  two  waves  corre- 
spond to  motions  of  the  light-transmitting  medium  in  opposite 
directions.  The  dark  bands,  then,  of  our  experiment  are  sim- 
ply the  places  at  which  the  two  beams  reflected  from  the  two 
surfaces  of  the  air  film  neutralize  or  destroy  each  other,  while 
the  light  bands  correspond  to  the  places  at  which  the  two 
beams  reenforce  each  other  and  thus  produce  illumination  of 
double  intensity.  The  position  of  the  second  dark  band  c 
must  of  course  be  determined  by  the  fact  that  the  distance 
from  c  to  k  and  back  (see  Fig.  390)  is  a  wave  length  more 
than  from  a  to  i  and  back,  and  so  on  down  the  wedge.  This 


Interference 

Reinforcement 

Interference 

Re  enforcement 

Interference 

Reenforcement 

Interference 

Reenforcement 


FIG.  390.  Explanation  of  formation  of  dark  and 
light  bands  by  interference  of  light  waves 


THE  NATUKE  OF  LIGHT  367 

phenomenon  of  the  interference  of  light  is  met  with  in  many 
different  forms,  and  in  every  case  the  wave  theory  furnishes 
at  once  a  wholly  satisfactory  explanation  of  the  observed 
effects,  while  the  corpuscular  theory,  on  the  other  hand,  is 
unable  to  account  for  any  of  these  interference  effects  with- 
out the  most  fantastic  and  violent  assumptions.  Hence  the 
corpuscular  theory  is  now  practically  abandoned,  and  light  is 
universally  regarded  by  physicists  as  a  form  of  wave  motion. 

428.  The  ether.    We  have   already  indicated  that  if  the 
wave  theory  is  to  be  accepted,  we  must  conceive,  with  Huy- 
gens,  that  all  space  is  filled  with  a  medium,  called  the  ether, 
in  which  the  waves  can  travel.    This  medium  cannot  be  like 
any  of  the  ordinary  forms  of  matter;    for  if  any  of  these 
forms  existed  in  interplanetary  space,  the  planets  and  the 
other  heavenly  bodies  would  certainly  be  retarded  in  their 
motions.    As  a  matter  of  fact,  in  all  the  hundreds  of  years 
during  which  astronomers  have  been  making  accurate  obser- 
vations of  the  motions  of  heavenly  bodies  no  such  retarda- 
tion has  ever  been  observed.    The  medium  which  transmits 
light  waves  must  therefore  have  a  density  which  is  infinitely 
small  even  in  comparison  with  that  of  our  lightest  gases. 

Further,  in  order  to  account  for  the  transmission  of  light 
through  transparent  bodies,  it  is  necessary  to  assume  that  the 
ether  penetrates  not  only  all  interstellar  spaces  but  all  inter- 
molecular  spaces  as  well. 

429.  Wave  length  of  yellow  light.    Although  light,  like  sound,  is  a 
form  of  wave  motion,  light  waves  differ  from  sound  waves  in  several 
important  respects.   In  the  first  place,  an  analysis  of  the  preceding  experi- 
ment, which  seems  to  establish  so  conclusively  the  correctness  of  the 
wave  theory,  shows  that  the  wave  length  of  light  is  extremely  minute 
in  comparison  with  that  of  ordinary  sound  waves.   The  wave  length  of 
the  yellow  light  used  in  that  experiment  is  .00006  centimeter  (about 

40,000  incn> 

The  number  of  vibrations  per  second  made  by  the  little  particles  which 
send  out  the  light  waves  may  be  found,  as  in  the  case  of  sound,  by 


868       NATUKE  AND  PKOPAGATION  OF  LIGHT 


dividiug  the  velocity  by  the  wave  length.  Since  the  velocity  of  light  is 
30,000,000,000  centimeters  per  second  and  the  wave  length  is  .00006 
centimeter,  the  number  of  vibrations  per  second  of  the  particles  which 
emit  yellow  light  has  the  enormous  value  500,000,000,000,000. 

430.  Wave  theory  explanation  of  refraction.  Let  one  look  ver- 
tically down  upon  a  glass  or  tall  jar  full  of  water  and  place  his  finger 
on  the  side  of  the.  glass  at  the  point  at  which  the  bottom  appears  to 
be,  as  seen  through  the  water  (Fig.  391).  In  every  case  it  will  be 
found  that  the  point  touched  by  the  finger  will  be 
about  one  fourth  of  the  depth  of  the  water  above 
the  bottom. 


According  to  the  wave  theory  this  effect  is 
due  to  the  fact  that  the  speed  of  light  is  less 
in  water  than  in  air.  Thus,  consider  a  wave 
which  originates  at  any  point  P  (Fig.  392) 
beneath  a  surface  of  water  and  spreads  from 
that  point  with  equal  speed  in  all  directions. 
At  the  instant  at  which  the  front  of  this  wave 
first  touches  the  surface  at  o  it  will,  of  course, 


FIG. 391.  Appar- 


be  of  spherical  form,  having  P  as  its  center,     ent  elevation  of 

Let  aob  be  a  section  of  this  sphere.    An  in-     th®  ,bo"om  of  a 

body  of  water 
stant  later,  if  the  speed  had  not  changed  in 

passing  into  air,  the  wave  would  have  still  had  P  as  its 
center,  and  its  form  would  have  coincided  with  the  dotted 
line  cOjd,  so  drawn  that  ac,  oo^  and  bd  are  all  equal.  But  if 
the  velocity  in  air  is  greater  than  in  water,  then  at  the  instant 
considered  the  disturbance  will  have  reached  some  point  o2 
instead  of  o^  and  hence  the  emerging  wave  will  actually  have 
the  form  of  the  heavy  line  co2d  instead  of  the  dotted  line  co^d. 
Now  this  wave  co^d  is  more  curved  than  the  old  wave  aob, 
and  hence  it  has  its  center  at  some  point  P'  above  P.  In  other 
words,  the  wave  has  bulged  upward  in  passing  from  water 
into  air.  Therefore,  when  a  section  of  this  wave  enters  the 
eye  at  E,  the  wave  appears  to  originate  not  at  P  but  at  P', 
for  the  light  actually  comes  to  the  eye  from  P1  as  a  center 


THE  NATURE  OF  LIGHT 


369 


rather  than  from  P.  We  conclude,  therefore,  that  if  light 
travels  more  slowly  in  water  than  in  air,  all  objects  beneath  the 
surface  of  water  ought  to  appear  nearer  to  the  eye  than  they 
actually  are.  This  is  precisely  what  we  found  to  be  the  case 
in  our  experiment. 

Furthermore,  since  when  the  eye  is  in  any  position  other 
than  E,  for  example  E\  the  light  travels  to  it  over  the  broken 
path  PdE\  the  construction  shows  that  light  is  always  bent 
away  from  the  perpendicu- 
lar when  it  passes  obliquely 
into  a  medium  in  which  the 
speed  is  greater.  If  it  had 
passed  into  a  medium  of  less 
speed,  the  point  P  would 
have  appeared  depressed 
below  its  natural  position, 
because  the  wave,  on  emerg- 
ing into  the  slower  medium, 
instead  of  bulging  upward 
would  be  flattened,  and 
therefore  would  have  its 
center  of  curvature,  or 
apparent  point  of  origin, 
below  P ;  hence  the  oblique  rays  would  have  appeared  to  be  bent 
toward  the  perpendicular,  as  we  found  in  §  423  to  be  the  case. 

431.  The  ratio  of  the  speeds  of  light  in  air  and  water.  The 
experiment  with  the  tall  jar  of  water  in  §  430  not  only  indi- 
cates qualitatively  that  the  speed  of  light  in  air  is  greater 
than  in  water,  but  it  furnishes  a  simple  means  of  determining 
the  ratio  of  the  two  speeds.  Thus,  in  Fig.  392  the  line  oo2 
represents  just  how  far  the  wave  travels  in  air  while  it  is 

traveling  the  distance  ac  (=  oo^)  in  water.    Hence  —2  is  the 

°°\ 
ratio  of  the  speeds  of  light  in  air  and  in  water. 


FIG.  392.  Representing  a  wave  emerging 
from  water  into  air 


370        NATUKE  AND  PROPAGATION  OF  LIGHT 


Now  the  curvatures  of  the  arcs  cod  and  cod  are  measured 


by  the  reciprocals  of  their  respective  radii 

i   1 
Curvature  of 


that  is, 


Curvature  of  co^d 


dP 


dP' 


(1) 


Now  when  the  arcs  are  small,  a  condition  which  in  general 
is  realized  in  experimental  work,  their  curvatures  are  propor- 
tional to  the  extent  to  which  they  bulge  out  from  the  straight 
line  cod^ ;  that  is, 


Curvature  of  co^d 


Curvature  of  co^d 
From  (1)  and  (2)  we  get 
Speed  in  air 


_  speed  in  air 
speed  in  water 


dP 


Speed  in  water      dP' 


(2) 


(3) 


*  Construct  an  angle  of  45°  (Fig.  393,  (1)).  Its  arc  contains  45°  and  the 
angle  formed  by  the  tangents  £,  t'  is  45°.  Now  with  a  radius  three  times  as 
great  (Fig.  393,  (2))  draw  an  arc  whose 
length  is  equal  to  that  of  the  arc  in 
Fig.  393  (1).  Since  the  radius  is  three 
times  as  great,  this  arc  contains  15°, 
and  the  angle  formed  by  the  tangents 
is  15°.  From  this  we  see  that  the  arc 
whose  radius  is  three  times  as  great 
curves,  or  changes  its  direction,  one 
third  as  fast ;  that  is,  the  change  in 

curvature  of  an  arc  of  given  length  varies  inversely  with  the  radius.  In  gen- 
eral then,  the  curvature  of  an  arc  is  measured  by  the  reciprocal  of  its  radius. 

t  oc  (Fig.  394)  is  a  mean  proportional  between  the  two 
segments  of  the  diameter  ;  hence  ao  x  od  =  oc2.  For  very 
small  arcs  od  is  practically  equal  to  the  diameter  £r.  Hence 


FIG.  393 


ao  = 


2r 


oc2      1 

or  ao  =  —  x  - 
2        r 


Therefore  ao  is  proportional  to 


_.     That  is,  the  distances  to  which  two  small  arcs  having  a 

r 

common  chord  bulge  out  from  the  chord  are  proportional  to 

the  respective  curvatures  of  the  arcs. 


FIG.  394 


THE  NATURE  OF  LIGHT  371 

But  in  looking  vertically  downward,  as  in  the  experiment 

dP  ,  oP     , 

with  the  iar  of  water,  -—-  becomes  — ;   hence, 

dP'  oP' 

Speed  in  air        _  oP  _  real  depth 
Speed  in  water      oP'      apparent  depth 

But  in  our  experiment  we  found  that  the  bottom  was  appar- 

oP      4 
ently  raised  one  fourth  of  the  depth ;  that  is,  that  — -  =  -  • 

We  conclude,  therefore,  that  light  travels  three  fourths  as 
fast  in  water  as  in  air. 

The  fact  that  the  value  of  this  ratio,  as  determined  by  this 
indirect  method,  is  exactly  the  same  as  that  found  by  Foucault 
and  Michelson  (see  opposite  p.  358)  by  direct  measurement 
(§419)  furnishes  one  of  the  strongest  proofs  of  the  correct- 
ness of  the  wave  theory. 

432.  Index  of  refraction.    The  ratio  of  the  speed  of  light  in 
air  to  its  speed  in  any  other  medium  is  called  the  index  of  refrac- 
tion of  that  medium.   It  is  evident  that  the  method  employed 
iii  the  last  paragraph  for  determining  the  index  of  refraction 
of  water  can   be  easily  applied  to  any  transparent  medium 
whether  liquid  or  solid.*    The  refractive  indices  of  some  of 
the  commoner  substances  are  as  follows: 

Water 1.33      Crown  glass 1.53 

Alcohol 1.36      Flint  glass 1.67 

Turpentine 1.47       Diamond 2.47 

433.  Light  waves  are  transverse.    Thus  far  we  have  discov- 
ered but  two  differences  between  light  waves  and  sound  waves ; 
namely,  the  former  are  disturbances  in  the  ether  and  are  of 
vary  short  wave  length,  while  the  latter  are  disturbances  in 

*  To  show  the  extreme  beauty,  simplicity,  and  accuracy  of  this  method 
of  getting  index  of  refraction  it  is  suggested  that  the  teacher  use  the  following 
method  in  his  laboratory  work. 

A  very  sharp  pencil  must  be  used  for  this  exercise.  Make  a  dot  P  on  a 
sheet  of  paper.  Put  the  glass  plate  (Fig.  395,  (1))  on  the  sheet  so  that  the 


372       NATURE  AND  PROPAGATION  OF  LIGHT 


ordinary  matter  and  are  of  relatively  great  wave  length.  There 
exists,  however,  a  further  radical  difference  which  follows  from 
a  capital  discovery  made  by  Huygens  (see  opposite  p.  364)  in 
the  year  1690.  It  is  this :  While  sound  waves  consist,  as  we 
have  already  seen,  of  longitudinal  vibrations  of  the  particles 
of  the  transmitting  medium,  that  is,  vibrations  back  and  forth 
in  the  line  of  propagation  of  the  wave,  light  waves  are  like 
the  water  waves  of  Fig.  346,  p.  324,  in  that  they  consist  of 
transverse  vibrations,  that  is,  vibrations  of  the  medium  at 
right  angles  to  the  direction  of  the  line  of  propagation. 

In  order  to  appreciate  the  difference  between  the  behavior 
of  waves  of  these  two  types  under  certain  conditions,  conceive 

edge  of  the  label  pasted  around  the  edge  of  the  glass  coincides  with  the  dot 
(or  in  case  a  prism  (Fig.  395,  (2))  is  used,  let  the  apex  P  coincide  with  the  dot). 
Draw  the  base  line  ef  and  the  other  sides  of  the  glass,  holding  it  firmly  down 
meanwhile.  Be  sure  that 
at  no  time  during  the 
exercise  does  the  glass 
slip  the  slightest  from 
its  first  position.  Lay  a 
ruler  upon  the  paper  in 
a  slantwise  position  cd 
(not  touching  the  glass), 
and,  with  one  eye  closed, 
make  its  edge  point  ex- 
actly at  the  apparent 
position  of  P  as  seen 
through  the  glass.  If  you 
are  now  sure  that  your 
ruler  did  not  push  the 
glass  out  of  position, 
draw  a  line  cd  with  the 

sharp  pencil.  Similarly,  draw  another  line  ab  about  as  far  to  the  right  of  the 
center  as  cd  is  to  the  left.  Remove  your  glass  and  complete  the  drawing  §£ 
indicated  in  the  diagram. 

P'  is  the  apparent  position  of  P.  As  you  have  already  learned  from  your 
text,  the  ratio  of  the  velocities  of  light  in  air  and  glass  is  found  by  dividing 
dP  by  dP'.  Measure  these  distances  very  carefully  to  0.1  mm.,  and  calculate 
the  index  of  refraction  to  two  decimal  places.  Make  two  or  three  more  trials 
and  compare  results. 


FIG.  395.   Index  of  refraction 


THE  NATURE  OF  LIGHT  373 

of  transverse  waves  in  a  rope  being  made  to  pass  through  two 
gratings  in  succession,  as  in  Fig.  396.  So  long  as  the  slits  in 
both  gratings  are  parallel  to  the  plane  of  vibration  of  the 
hand,  as  in  Fig.  396,  (1),  the  waves  can  pass  through  them 
with  perfect  ease ;  but 
if  the  slits  in  the  first 
grating  P  are  parallel  to 
the  direction  of  vibra- 
tion, while  those  of  the 
second  grating  Q  are 
turned  at  right  angles 

to  this  direction,  as  in 

_,.       nf.~     x~x     .,    .          .  FIG.  396.    Transverse  waves  passing 

Kg.  896,  (2),  it  is  evi-  through  site 

dent    that    the    waves 

will  pass  readily  through  P,  but  will  be  stopped  completely 

by  Q,  as  shown  in  the  figure.    In  other  words,  these  gratings 

P  and  Q  will  let  through  only  such  vibrations  as  are  parallel 

to  the  direction  of  their  slits. 

If,  on  the  other  hand,  a  longitudinal  instead  of  a  transverse 
Wave  —  such,  for  example,  as  a  sound  wave  —  had  approached 
such  a  grating,  it  would  have  been  as  much  transmitted  in 
one  position  of  the  grating  as  in  another,  since  a  to-and-fro 
motion  of  the  particles  can  evidently  pass  through  the  slits 
with  exactly  the  same  ease,  no  matter  how  they  are  turned. 

Now  two  crystals  of  tourmaline  are  found  to  behave  with 
respect  to  light  waves  just  as  the  two  gratings  behave  with 
respect  to  the  waves  on  the  rope. 

Let  one  such  crystal  a  (Fig.  397)  be 
held  in  front  of  a  small  hole  in  a  screen 
through  which   a   beam    of    sunlight   is     FlG>  39L    Tourmaline  tongs 
passing  to  a  neighboring  wall ;  or,  if  the 

sun  is  not  shining,  simply  let  the  crystal  be  held  between  the  eye  and  a 
source  of  light.  The  light  will  be  readily  transmitted,  although  some- 
what diminished  in  intensity.  Then  let  a  second  crystal  b  be  held  in 
line  with  the  first.  The  light  will  still  be  transmitted,  provided  the  axes  of 


374       NATURE  AND  PROPAGATION  OF  LIGHT 


the  crystals  are  parallel,  as  shown  in  Fig.  308.  When,  however,  one  of  the 
crystals  is  rotated  in  its  ring  through  90°  (Fig.  399),  the  light  is  cut  off. 
This  shows  that  a 
crystal  of  tourma- 
line is  capable  of 
transmitting  only 


FIG.  398.    Light  pass- 
ing through  tourmaline 


FIG.  399.    Light  cut  off 

by   crossed    tourmaline 

crystals 


light  which  is  vibra- 
ting in  one  particu- 
lar plane. 

From  this  ex- 
periment, there- 
fore, we  are  forced  to  conclude  that  light  waves  are  transverse 
rather  than  longitudinal  vibrations.  The  experiment  illustrates 
what  is  technically  known  as  the  polarization  of  light,  and 
the  beam  which,  after  passage  through  «,  is  unable  to  pass 
through  b  if  the  axes  of  a  and  b  are  crossed,  is  known  as  a 
polarized  beam.  It  is,  then,  the  phenomenon  of  the  polariza- 
tion of  light  upon  which  we  base  the  conclusion  that  light 
waves  are  transverse. 

434.  Intensity  of  illumination.  Let  four  candles  be  set  as 
close  together  as  possible  in  such  a  position  B  as  to  cast  upon  a  white 
screen  C,  placed  in  a  well-darkened  room,  a  shadow  of  an  opaque  object  O 
(Fig.  400).  Let  one  single  candle  be  placed  in  a  position  A  such  that 
it  will  cast  another  shadow  of  0  upon  the  screen.  Since  light  from  A 
falls  on  the  shadow  cast  by  B,  and  light  from  B  falls  on  the  shadow 
cast  by  A,  it  is  clear  that  the  two 
shadows  will  appear  equally  dark 
only  when  light  of  equal  intensity 
falls  on  each ;  that  is,  when  A  and 
B  produce  equal  illumination  upon 
the  screen.  Let  the  positions  of  A 
and  B  be  shifted  until  this  condition 
is  fulfilled.  Then  let  the  distances 

from  B  to  C  and  from  A  to  C  be  measured.  If  all  five  candles  are  burning 
with  flames  of  the  same  size,  the  first  distance  will  be  found  to  be  just 
twice  as  great  as  the  second.  Hence  the  illumination  produced  upon 
the  screen  by  each  one  of  the  candles  at  B  is  but  one  fourth  as  great  as 
that  produced  on  the  screen  by  one  candle  at  A,  one  half  as  far  away. 


FIG.  400.    Rumford's  photometer 


THE  NATURE  OF  LIGHT  375 

The  above  is  the  direct  experimental  proof  that  the  intensity  of 
illumination  varies  inversely  as  the  square  of  the  distance  from 
the  source. 

The  theoretical  proof  of  the  law  is  furnished  at  once  by 
Fig.  401,  for  since  all  the  light  which  falls  from  the  candle  L 
on  A  is  spread  over  four  times  as  large  an  area  when  it  reaches 
B,  twice  as  far  away,  and  over  nine  times  as  large  an  area 


FIG.  401.    Proof  of  law  of  inverse  squares 


when  it  reaches  (7,  three  times  as  far  away,  obviously  the  in- 
tensities at  B  and  at  C  can  be  but  one  fourth  and  one  ninth  as 
great  as  at  A. 

The  above  method  of  comparing  experimentally  the  inten- 
sities of  two  lights  was  first  used  by  Count  Rumford.  The 
arrangement  is  therefore  called  the  Rumford  photometer  (light 
measurer). 

435.  Candle  power.  The  last  experiment  furnishes  a  method 
of  comparing  the  light-emitting  powers  of  various  sources  of 
light.  For  example,  suppose  that  the  four  candles  at  B  are 
replaced  by  a  gas  flame,  and  that  for  the  condition  of  equal 
illumination  upon  the  screen  the  two  distances  BC  and  AC  are 
the  same  as  above,  namely,  2  to  1.  We  should  then  know  that 
the  gas  flame,  which  is  able  to  produce  the  same  illumination 
at  a  distance  of  two  feet  as  a  candle  at  a  distance  of  one  foot, 
has  a  light-emitting  power  equal  to  four  candles.  In  general, 
then,  the  candle  powers  of  any  tivo  sources  which  produce  equal 
illumination  on  a  given  screen  are  directly  proportional  to  the 
squares  of  the  distances  of  the  sources  from  the  screen. 

It  is  customary  to  express  the  intensities  of  all  sources  of 
light  in  terms  of  candle  power,  one  candle  power  being  denned 
as  the  amount  of  light  emitted  by  a  sperm  candle  J-  inch  in 


376       NATURE  AND  PROPAGATION  OF  LIGHT 

diameter  and  burning  120  grains  (7.776  grams)  per  hour.  The 
candle  power  of  an  ordinary  gas  flame  burning  5  cubic  feet 
per  hour  is  from  16  to  25,  depending  on  the  quality  of  the  gas. 
A  standard  candle  at  a  distance  of  1  foot  gives  an  intensity 
of  illumination  called  &  foot-candle.  A  100-candle-power  lamp, 
for  example,  at  a  distance  of  1  foot  gives  an  intensity  of  illu- 
mination of  100  foot-candles ;  at  2  feet,  of  25  foot-candles ;  at 
5  feet,  of  4  foot-candles ;  and  at  10  feet,  of  1  foot-candle. 

436.  Bunsen's  photometer.  Let  a  drop  of  oil  or  melted  paraffin  be 
placed  in  the  middle  of  a  sheet  of  unglazed  white  paper  to  render  it 
translucent.  Let  the  paper  be  held  near  a  window  and  the  side  away 
from  the  window  observed.  The  oiled  spot  will  appear  lighter  than  the 
remainder  of  the  paper.  Then  let  the  paper  be  held  so  that  the  side 
nearest  the  window  may  be  seen.  The  oiled  spot  will  appear  darker 
than  the  rest  of  the  paper.  We  learn,  therefore,  that  when  the  paper  is 
viewed  from  the  side  of  greater  illumination,  the  oiled  spot  appears  dark ; 
but  when  it  is  viewed  from  the  side  of  lesser  illumination,  the  spot  appears  light. 
If,  then,  the  two  sides  of  the  paper  are  equally  illuminated,  the  spot 
ought  to  be  of  the  same  brightness  when  viewed  from  either  side.  Let 
the  room  be  darkened  and  the  oiled  paper  placed  between  two  gas  flames, 
two  electric  lights,  or  any  two  equal  sources  of  light.  It  will  be  observed 
that  when  the  paper  is  held  closer  to  one  than  the  other,  the  spot  will 
appear  dark  when  viewed  from  the 
side  next  the  closer  light;  but  if  it 
is  then  moved  until  it  is  nearer  the 
other  source,  the  spot  will  change 
from  dark  to  light  when  viewed  always 
from  the  same  side.  It  is  always  pos-  ^IG.  402.  Bunsen's  photometer 
sible  to  find  some  position  for  the  oiled 

paper  at  which  the  spot  either  disappears  altogether  or  at  least  appears 
the  same  when  viewed  from  either  side.  This  is  the  position  at  which 
the  illuminations  from  the  two  sources  are  equal.  Hence,  to  find  the 
candle  power  of  any  unknown  source  it  is  only  necessary  to  set  up  a 
candle  on  one  side  and  the  unknown  source  on  the  other,  as  in  Fig.  402, 
and  to  move  the  spot  A  to  the  position  of  equal  illumination.  The  can- 
dle power  of  the  unknown  source  at  C  will  then  be  the  square  of  the 
distance  from  C  to  A,  divided  by  the  square  of  the  distance  from  B  to  A. 

This  arrangement  is  known  as  the  Bunsen  photometer. 


THE  NATURE  OF  LIGHT  377 


QUESTIONS  AND  PROBLEMS 

1.  Distinguish  between  candle  power,  intensity  of  light,  and  inten- 
sity of  illumination. 

2.  How  many  candles  will  be  required  to  produce  the  same  intensity 
of  illumination  at  2  m.  that  is  produced  by  1  candle  at  30  cm.  ? 

3.  A  500-candle-power  lamp  is  placed  50  m.  from  a  darkly  shaded 
place  along  the  street.    At  what  distance  would  a  100-candle-power 
lamp  have  to  be  to  produce  the  same  intensity  of  illumination  ? 

4.  If  a  2-candle-power  light  at  a  distance  of  1  ft.  gives  enough 
illumination  for  reading,  how  far  away  must  a  3 2-candle-power  lamp 
be  placed  to  make  the  same  illumination?  How  strong  a  lamp  should 
be  used  at  a  distance  of  8  ft.  from  the  book  ? 

5.  A  Bunsen  photometer  placed  between  an  arc  light  and  an  incan- 
descent light  of  32  candle  power  is  equally  illuminated  on  both  sides 
when  it  is  10  ft.  from  the  incandescent  light  and  36  ft.  from  the  arc 
light.    What  is  the  candle  power  of  the  arc  ? 

6.  A  5-candle-power  and  a  30-candle-power  source  of  light  are  2  m. 
apart.  Where  must  the  oiled  disk  of  a  Bunsen  photometer  be  placed  in 
order  to  be  equally  illuminated  on  the  two  sides  by  them  ? 

7.  If  the  sun  were  at  the  distance  of  the  moon  from  the  earth,  in- 
stead of  at  its  present  distance,  how  much  stronger  would  sunlight  be 
than  at  present?   The  moon  is  240,000  mi.  and  the  sun  93,000,000  mi. 
from  the  earth. 

8.  If  a  gas  flame  is  300  cm.  from  the  screen  of  a  Rumford  photom- 
eter, and  a  standard  candle  50  cm.  away  gives  a  shadow  of  equal  inten- 
sity, what  is  the  candle  power  of  the  gas  flame  ? 

9.  Will  a  beam  of  light  going  from  water  into  flint  glass  be  bent 
toward  or  away  from  the  perpendicular  drawn  into  the  glass  ? 

10.  When  light  passes  obliquely  from  air  into  carbon  bisulphide  it  is 
bent  more  than  when  it  passes  from  air  into  water  at  the  same  angle. 
Is  the  speed  of  light  in  carbon  bisulphide  greater  or  less  than  in  water? 

11.  If  light  travels  with  a  velocity  of  186,000  miles  per  sec.  in  air, 
what  is  its  velocity  in  water,  in  crown  glass,  and  in  diamond?  (See  table 
of  indices  of  refraction,  p.  371.) 


CHAPTER  XIX 

IMAGE  FORMATION 
IMAGES  FORMED  BY  LENSES 

437.  Focal  length  of  a  convex  lens.  Let  a  convex  lens  be  tfeld 
in  the  path  of  a  beam  of  sunlight  which  enters  a  darkened  room,  where 
it  is  made  plainly  visible  by  means  of  chalk  dust  or  smoke.  The  beam 
will  be  found  to  converge  to  a  focus  F,  as  shown  in  Fig.  403. 

The  explanation  is  as  follows:  The  waves  from  the  sun 
or  any  distant  object  are  without  any  appreciable  curvature 
when  they  strike  the  lens; 
that  is,  they  are  so-called 
plane  waves  (see  Fig.  403). 
Since  the  speed  of  light  is  less 

in  glass  than  in  air,  the  cen-     Fic"  403'  prhlciPal  focusFand  focal 

length  CF  of  a  convex  lens 
tral  portion  of  these  waves 

is  retarded  more  than  the  outer  portions  in  passing  through 
the  lens.  Hence,  on  emerging  from  the  lens  the  waves  are  con- 
cave instead  of  plane,  and  close  in  to  a  center  or  focus  at  F. 

A  second  way  of  looking  at  the  phenomenon  is  to  think 
of  the  "  rays  "  which  strike  the  lens  as  being  bent  by  it,  in 
accordance  with  the  laws  given  in  §  423,  so  that  they  all 
pass  through  the  point  F. 

The  line  through  the  point  C  (the  optical  center)  of  the 
lens,  perpendicular  to  its  faces,  is  called  the  principal  axis. 

The  point  F  at  which  rays  parallel  to  the  principal  axis 
(incident  plane  waves)  are  brought  to  a  focus  is  called  the 
principal  focus. 

The  distance  CF  from  the  center  of  the  lens  to  the  prin- 
cipal focus  is  called  the  focal  length  (/)  of  the  lens. 

378 


IMAGES  FORMED  BY  LENSES 


379 


FIG.  404.    Focal  plane  of  a  convex  lens 


The  plane  F'FF"  (Fig.  404)  m  which  plane  waves  (parallel 
rays)  coming  to  the  lens  from  slightly  different  directions,  as 
from  the  top  and  bottom  of 
a  distant  house,  all  have 

their  foci    F',   F",   etc.   is       //UmUWmffiqttttffl™  -F 

called   the  focal  plane    of 
the  lens. 

Since   the   curvature   of 
any  arc  is  defined  as  the  reciprocal  of  its  radius  (see  footnote, 
p.  370),   the  curvature  which  a  lens  impresses  on  an  incident 

plane  wave  is  equal  to  -•     Moreover,   no   matter  what  the 

J 
curvature  of  an  incident  wave  may  be,  the  lens  will  ahvays 

change  the  curvature  by  the  same  amount,  -• 

c/ 

Let  the  focal  length  of  a  convex  lens  be  accurately  determined  by 
measuring  the  distance  from  the  middle  of  the  lens  to  the  image  of  a 
distant  house. 

438.  Conjugate  foci.  If  a  point  source  of  light  is  placed  at 
F  (Fig.  403),  it  is  obvious  that  the  light  which  goes  through 
the  lens  must  exactly  retrace  its  former  path ;  that  is,  its 


FIG.  405.    Conjugate  foci 

waves  will  be  rendered  plane  or  its  rays  parallel  by  the  lens. 
But  if  the  point  source  is  at  a  distance  D0  greater  than  / 
(Fig.  405),  then  the  waves  upon  striking  the  lens  have  a 

curvature  —  (sin<3e  the  curvature  of  an  arc  is  defined  as 
the  reciprocal  of  its  radius),  which  is  less  than  their  former 
curvature,  -.  Since  the  lens  was  able  to  subtract  all  the 


380  IMAGE  FORMATION 

curvature  from  waves  coming  from  F  and  render  them  plane, 
by  subtracting  the  same  curvature  from  the  flatter  waves 
from  P  it  must  render  them  concave  ;  that  is,  the  rays  after 
passing  through  the  lens  are  converging  and  intersect  at  P'. 
If  the  source  is  placed  at  P',  obviously  the  rays  will  meet  at 
P.  Points  such  as  P  and  P',  so  related  that  one  is  the  image 
of  the  other,  are  called  conjugate  foci. 

439.  Formula  for  conjugate  foci  ;  secondary  foci.  Since  in 
Fig.  405  the  curvature  of  the  wave  when  it  emerges  from 
the  lens  is  opposite  in  direction  to  its  curvature  when  it 

reaches  the  lens,  the  sum  of  these  curvatures,  --  1  --  ,  repre- 
sents the  power  of  the  lens  to  change  the  curvature  of  the 
incident  wave,  which  by  §  437  is  —  •  Hence 

' 


that  is,  the  sum  of  the  reciprocals  of  the  distances  of  the  conju- 
gate foci  from  the  lens  is  equal  to  the  reciprocal  of  the  focal 
length.  If  D0=  Df,  then  the  equation  shows  that  both  D0  and 
D{  are  equal  to  2/. 

The  two  conjugate  foci  S  and  S1  which  are  at  equal  dis- 
tances from  the  lens  are  called  the  secondary  foci,  and  their 
distance  from  the  lens  is  twice  the  focal  distance. 


FIG.  406.    Formation  of  a  real  image  by  a  lens 

440.  Images  of  Objects.  Let  a  candle  or  electric-light  bulb  be 
placed  between  the  principal  focus  F  and  the  secondary  focus  S  at  PQ 
(Fig.  406),  and  let  a  screen  be  placed  at  P'Q'.  An  enlarged  inverted 
image  will  be  seen  upon  the  screen. 


IMAGES  FORMED  BY  LENSES  381 

This  image  is  formed  as  follows:  All  the  light  which 
strikes  the  lens  from  the  point  P  is  brought  together  at  a 
point  P'.  The  location  of  this  image  P'  must  be  on  a  straight 
line  drawn  from  P  through  C ;  for  any  ray  passing  through  C 
will  remain  parallel  to  its  original  direction,  since  the  portions  of 
the  lens  through  which  it  enters  and  leaves  may  be  regarded  as 
small  parallel  planes  (see  §  423).  The  image  P'Q'  is  therefore 
always  formed  between  the  lines  drawn  from  P  and  Q  through  C. 
If  the  focal  length  /  and  the  distance  of  the  object  D0  are 
known,  the  distance  of  the  image  D.  may  be  obtained  easily 
from  formula  (1). 

The  position  of  the  image  may  also  be  found  graphically  as 
follows :  Of  the  cone  of  rays  passing  from  P  to  the  lens,  that 


FIG.  407.    Ray  method  of  constructing  an  image 

ray  which  is  parallel  to  the  principal  axis  must,  by  §  43  7, 
pass  through  the  principal  focus  F  .  The  intersection  of  this 
line  with  the  straight  line  through  C  locates  the  image  Pr 
(see  Fig.  407).  Q',  the  image  of  Q,  is  located  similarly. 

441.  Size  of  image.  Since  the  image  and  object  are  always 
between  the  intersecting  straight  lines  PPf  and  QQ',  the 
similar  triangles  PCQ  and  P'CQ'  show  that 


,       .     Length  of  object  _  distance  of  object  from  lens 
Length  of  image      distance  of  image  from  lens 

It  may  be  seen  from  Fig.  407,  as  well  as  from  formulas  (1) 
and  (2),  that 

1.  When  the  object  is  at  S  the  image  is  at  £',  and  image 
and  object  are  of  the  same  size. 


382 


IMAGE  FORMATION 


FIG.  408.  Virtual  image  formed 
by  a  convex  lens 


2.  As  the  object  moves  out  from  S  to  a  great  distance  the 
image  moves  from  Sf  up  to  F'9  becoming  smaller  and  smaller. 

3.  As  the  object  moves  from  S 
up  to  F  the  image  moves  out  to  a 
very  great  distance  to  the  right, 
becoming  larger  and  larger. 

4.  When  the  object  is  at  F  the 
emerging  waves  are  plane    (the 
emerging  rays  are  parallel),  and 
no  real  image  is  formed. 

442.  Virtual  image.    We  have  seen  that  when  the  object  is 
at  F  the  waves  after  passing  through  the  lens  are  plane.    If, 
then,  the  object  is  nearer  to 

the  lens  than  F,  the  emerg- 
ing waves,  although  reduced 
in  curvature,  will  still  be  con- 
vex, and,  if  received  by  an  - , 

eye  at  E,  will  appear  to  come 

/  .          *, r  ,„.        .  FIG.  409.     Ray   method    of    locating 

from  a  point  P*  (Fig.  408).        a  virtual  image  in  a  convex  lens 

Since,  however,  there  is  actu- 
ally no  source  of  light  at  P',  this  sort  of  image  is  called  a 
virtual  image.     Such  an  image  cannot   be  projected  upon  a 
screen  as  a  real  image  can,  but  must  be  observed  by  an  eye. 

The  graphical  location  of  a  virtual  image 
may  be  accomplished  precisely  as  in  the  case 
of  a  real  image  (§  440).  It  will  be  seen  that 
in  this  case  (Figs.  408  and  409)  the  image 
is  enlarged  and  erect. 

443.  Image  in  concave  lens.   When  a  plane 
wave  strikes  a  concave  lens,  it  must  emerge 

as  a  divergent  wave,  since  the  middle  of  the  wave  is  retarded 
by  the  glass  less  than  the  edges  (Fig.  410).  The  point  F 
from  which  plane  waves  appear  to  come  after  passing  through 
such  a  lens  is  the  principal  focus  of  the  lens.  For  the  same 


FIG.  410.  Virtual 
focus  of    a   con- 
cave lens 


IMAGES  IN  MIRRORS 


383 


reason  .as  in  the  case  of  the  convex  lens  the  centers  of  the 
transmitted  waves  from  P  and  Q  (Fig.  411),  that  is,  the  images 
P1  and  Q',  must  lie  upon  the  lines  PC  and  QC;  and  since  the 


FIG.  411.  Image  in  a  concave  lens 


FIG.  412.    Ray  method  of  locating 
an  image  in  a  concave  lens 


curvature  is  increased  by  the  lens,  they  must  lie  closer  to  the 
lens  than  P  and  Q.  Fig.  411  shows  the  way  in  which  such  a 
lens  forms  an  image.  This  image  is  always  virtual,  erect,  and 
diminished.  .The  graphical  method  of  locating  the  image  is 
shown  in  Fig.  412. 

IMAGES  IN  MIRRORS 

444.  Image  of  a  point  in  a  plane  or  a  curved  mirror.    We 

are  all  familiar  with  the  fact  that  to  an  eye  at  E  (Fig.  413), 
looking  into  a  plane  mirror  mn,  a  pen- 
cil point  at  P  appears  to  be  at  some 
point  P'  behind  the  mirror.  We  are 
able  in  the  laboratory  to  find  experi- 
mentally the  exact  location  of  this 
image  P'  with  respect  to  P  and  the 
mirror,  but  we  may  also  obtain  this 
location  from  theory  as  follows :  Con- 
sider a  light  wave  which  originates  in 
the  point  P  (Fig.  413)  and  spreads  in 
all  directions.  Let  aob  be  a  section  of 
the  wave  at  the  instant  at  which  it 
reaches  the  reflecting  surface  mn.  An 
instant  later,  if  there  were  no  reflecting  surface,  the  wave 
would  have  reached  the  position  of  the  dotted  line  cofl. 


FIG.  413.    Wave   reflected 
from  a  plane  surface 


384 


IMAGE  FORMATION 


Since,  however,  reflection  took  place  at  win,  and  since  the 
reflected  wave  is  propagated  backward  with  exactly  the  same 
velocity  with  which  the  original  wave  would  have  been  prop- 
agated forward,  at  the  proper  instant  the  reflected  wave  must 
have  reached  the  position  of  the  line  co2d,  so  drawn  that  oo^ 
is  equal  to  ooz.  Now  the  wave  co^d  has  its  center  at  some 
point  P',  and  it  will  be  seen  that  P'  must  lie  just  as  far  below 
mn  as  P  lies  above  it,  for  cofl  and  co^d  are  arcs  of  equal  circles 

JXlM 


FIG.  414.    Wave  reflected  from  a 
convex  surface 


FIG.  415.    Wave    reflected 
from  a  concave  surface 


having  the  common  chord  cd.  For  the  same  reason,  also,  P' 
must  lie  on  the  perpendicular  drawn  from  P  through  mn. 
When,  then,  a  section  of  this  reflected  wave  co2d  enters  the 
eye  at  E,  the  wave  appears  to  have  originated  at  P'  and  not 
at  P,  for  the  light  actually  comes  to  the  eye  from  P'  as  a 
center  rather  than  from  P.  Hence  P1  is  the  image  of  P. 
We  learn,  therefore,  that  the  image  of  a  point  in  a  plane  mir- 
ror lies  on  the  perpendicular  drawn  from  the  point  to  the  mirror 
and  is  as  far  back  of  the  mirror  as  the  point  is  in  front  of  it. 
Precisely  the  same  construction  applied  to  curved  mirrors 
shows  at  once  (Fig.  414  and  Fig.  415)  that  the  image  of  a 
point  in  any  mirror,  plane  or  curved,  must  lie  on  the  perpen- 
dicular drawn  from  the  point  to  the  mirror ;  but  if  the  mirror 


IMAGES  IN  MIRRORS 


385 


is  convex,  the  image  is  nearer  to  it  than  is  the  point,  while  if  it  is 
concave,  the  image,  if  formed  behind  the  mirror  at  all  (that  is, 
if  it  is  virtual),  is  farther  from  the  mirror  than  is  the  point. 

445.  Construction  of  image  of  object  in  a  plane  mirror. 
The  image  of  an  object  in  a  plane  mirror  (Fig.  416")  may 
be  located  by  applying  the  law 

proved  above  for  each  of  its 
points,  that  is,  by  drawing  from 
each  point  a  perpendicular  to  the 
reflecting  surface  and  extending  it 
an  equal  distance  on  the  other  side. 
To  find  the  path  of  the  rays 
which  come  to  an  eye  placed  at  FIG.  416.  Construction  of  image  of 

,,  ,,    ,         ,  .  object  in  a  plane  mirror 

E  from  any  point  of  the  object, 

such  as  A,  we  have  only  to  draw  a  line  from  the  image  A'  of 
this  point  to  the  eye  and  connect  the  point  of  intersection 
of  this  line  with  the  mirror,  namely  C,  with  the  original 
point  A.  ACE  is  then  the  path  of  the  ray. 

Let  a  candle  (Fig.  417)  be  placed  exactly  as  far  in  front  of  a  pane  of 
window  glass  as  a  bottle  full  of  water  is  behind  it,  both  objects  being 
on  the  same  perpendicular  drawn  through 
the  glass.  The  candle  will  appear  to  be 
burning  inside  the  water.  This  explains  a 
large  class  of  familiar  optical  illusions,  such 
as  the  w  figure  suspended  in  mid-air,"  the 
"bust  of  a  person  without  a  trunk,"  the 
**  stage  ghost,"  etc.  In  the  last  case  the  illu- 
sion is  produced  by  causing  the  audience  to 
look  at  the  actors  obliquely  through  a  sheet 
of  very  clear  plate  glass,  the  edges  of  which 
are  concealed  by  draperies.  Images  of  strongly  illuminated  figures 
at  one  side  then  appear  to  the  audience  to  be  in  the  midst  of  the  actors. 

446.  Focal  length  of  a  curved  mirror  half  its  radius  of  curva- 
ture.   The  effect  of  a  convex  mirror  on  plane  waves  incident 
upon  it  is  shown  in  Fig.  418.     The  wave  which  would  at  a 


FIG.  417.  Position  of  image 
in  a  plane  mirror 


386 


IMAGE  FORMATION 


given  instant  have  been  at  co^d  is  at  cozd,  where  ool  =  oo2. 
The  center  F  from  which  the  waves  appear  to  come  to  the 
eye  E  is  the  focus 
of  the  mirror. 

Now  so  long 
as  the  arc  cod  is 
small  its  curva- 
ture may,  without 
appreciable  error, 
be  measured  by 
o^p  (see  footnote, 
p.  370);  that  is, 
by  the  departure 
of  the  curved 
line  cod  from  the 
straight  line  co^d. 


FIG.  418.   Reflection  of  a  plane  wave  from  a 
convex  mirror 

Since    o  o   was   made    equal   to   oo ,   we 


have  0^  =  2  o^o ;    that  is,  the  curvature  —  of  the  reflected 
wave   is   equal   to   twice    the    curvature   of   the   mirror,    or 

In  other  words,  the  focal  length  of 


1      0      1   '  ,     R 

-  =  2x-;   hence  /=- 


a  mirror  is  equal  to  one  half  its  radius. 

447.  Image  of  an  object  in  a  convex  mirror.    We  are  all 
familiar  with  the  fact  that  a   convex   mirror   always  forms 
behind  the  mirror  a  virtual, 
erect,  and  diminished  image. 
The  reason  for  this  is  shown 
clearly    in    Fig.  419.      The 
image  of  the  point  P  lies,  as 
in  plane  mirrors  (see  §  444), 
always  on  the  perpendicular 
to  the  mirror,  but  now  neces- 
sarily nearer  to  the  mirror  than  the  focus  F,  since,  as  the  point 
P  is  moved  from  a  position  very  close  to  the  mirror,  where 


SECTION  OF  A  ft MOVIE"  FILM  SHOWING  SECRETARY  or  WAR  BAKER 

TURNING   HIS   HEAD  TO   SPEAK   TO   GENERAL  PERSHING 

The  moving-picture  camera  makes  a  series  of  snapshots  upon  a  film,  usually  at 
the  rate  of  10  per  second.  The  film  is  drawn  past  the  lens  with  a  jerky  movement, 
being  held  at  rest  during  the  instant  of  exposure  and  moved  forward  while  the 
shutter  is  closed.  The  pictures  are  |-inch  high  and  1  inch  wide.  Since  1  foot  of 
film  per  second  is  drawn  past  the  lens,  a  reel  of  film  1000  feet  long  (the  usual  length) 
contains  16,000  pictures.  From  the  reel  of  negatives  a  reel  of  positives  is  printed 
for  use  in  the  projection  apparatus.  The  optical  illusion  of  "  moving  "  pictures  is 
made  possible  by  a  peculiarity  of  the  eye  called  persistence  of  vision.  To  illustrate 
this  let  a  firebrand  be  rapidly  whirled  in  a  circle.  The  spot  of  light  appears 
drawn  into  a  luminous  arc.  This  phenomenon  is  due  to  the  fact  that  we  continue 
to  see  an  object  for  a  small  fraction  of  a  second  after  the  image  of  it  disappears 
from  the  retina.  The  period  of  time  varies  somewhat  with  different  individuals. 
The  so-called  "moving"  pictures  do  not  move  at  all.  In  normal  projection 
16  brilliant  stationary  pictures  per  second  appear  in  succession  upon  the  screen, 
and  during  the  interval  between  the  pictures  the  screen  is  perfectly  dark.  It  is 
during  this  period  of  darkness  that  the  film  is  jerked  forward  to  get  the  next 
picture  into  position  for  projection.  The  eye,  however,  detects  no  period  of  ,dark- 
ness,  for  on  account  of  persistence  of  vision  it  continues  to  see  the  stationary 
picture  not  only  during  this  period  of  darkness  but  dimly  for  an  instant  even 
after  the  next  picture  appears  upon  the  screen.  This  causes  the  successive  station- 
ary pictures,  which  differ  but  slightly,  to  blend  smoothly  into  each  other  and  thus 
give  the  effect  of  actual  motion 


r 


5  6 

PHOTOGRAPHS  OF  SOUND  WAVES  HAVING  THEIR  ORIGIN  IN  AN  ELECTRIC 
SPARK  BEHIND  THE  MIDDLE  OF  THE  BLACK  DISK 

1.  A  spherical  sound  wave.  2.  The  same  wave  .00007  second  later.  3.  A  wave  re- 
flected from  a  plane  surface,  curvature  unchanged.  4.  A  wave  reflected  from  a 
convex  surface,  curvature  increased.  5.  The  source  at  the  focus  of  a  SO2  lens.  The 
photograph  shows  first,  the  original  wave  on  the  right ;  second,  the  reflected  wave, 
with  its  increased  curvature  ;  and  third,  the  transmitted  plane  wave.  6.  Source  at 
focus  of  a  concave  mirror ;  the  reflected  wave  is  plane.  (Taken  by  Professor  A.  L. 
Foley  and  Wilmer  H.  Souder,  of  the  University  of  Indiana) 


IMAGES  IN  MIRKORS 


387 


its  image  is  just  behind  it,  out  to  an  infinite  distance,  its  image 
moves  back  only  to  the  focal  plane  through  F.  Hence  the 
image  must  lie  somewhere  between  F  and  the  mirror.  The 
image  P'Q'  of  an  object  PQ  is  always  diminished,  because  it 
lies  between  the  converging  lines  PC  and  QC.  It  can  be 
located  by  the  ray  method  (Fig.  419)  exactly  as  in  the  case 
of  concave  lenses.  In  fact,  a  convex  mirror  and  a  concave  lens 
have  exactly  the  same  opti- 
cal properties.  This  is  be- 
cause each  always  increases 
the  curvature  of  the  incident 

waves  by  an  amount  -  • 

448.  Images  in  concave 
mirrors.  Let  the  images  ob- 
tainable with  a  concave  mirror 
be  studied  precisely  as  were 
those  obtainable  from  a  convex  lens.  It  will  be  found  that  exactly  the 
same  series  of  images  is  obtained :  when  the  object  is  between  the 
mirror  and  the  principal  focus,  the  image  is  virtual,  enlarged,  and 
erect;  when  it  is  at  the  focus  the  reflected  waves  are  plane,  that  is, 
the  rays  from  each  point  are  a  parallel  bundle  ;  when  it  is  between  the 


FIG.  420.    Real  image  of  candle  formed 
by  a  concave  mirror 


FIG.  421.    Method  of  formation  of  a  real  image  by  a  concave  mirror 

principal  focus  and  the  center  of  curvature,  the  image  is  inverted,  en- 
larged, and  real  (Figs.  420  and  421)  ;  when  it  is  at  a  distance  R  (=  oC) 
from  the  mirror,  the  image  is  also  at  a  distance  R  and  of  the  same  size 
as  the  object,  though  inverted ;  when  the  object  is  moved  from  R  out  to 


388 


IMAGE  FORMATION 


a  great  distance,  the  image  moves  from  C  up  to  F,  and  is  always  real, 
inverted,  and  diminished.  The  most  convenient  way  of  finding  the 
focal  length  is  to  find  where 
the  image  of  a  distant  object  is 
formed. 

We  learn,  then,  that  a  con- 
cave mirror  has  exactly  the 
optical  properties  of  a  con- 
vex lens.  This  is  because, 

like  the  convex  lens,  it  always    FlG'  422'  Ra7  method  of  locating  rea' 

J  image  in  a  concave  mirror 

diminishes  the  curvature   of 

the  waves.    The   same  formulas  hold  throughout,   and  the 

same  constructions  are  applicable  (see  Fig.  422). 

449.  Summary  for  lenses  and  spherical  mirrors.* 
1.  Real  images,  inverted  ;  virtual  images,  erect. 
The  length  of  all  images  is  given  by 

Ln      Dn 


where  L0  and  Lt-  denote  the  length  of  object  and  image  respec- 
tively, and  D0  and  Df  their  distances  from  the  lens  or  mirror. 

2.  Convex  lenses  and  concave  mirrors  have  the  same  optical  proper- 

ties (always  diminish  the  curvature  of  the  waves). 

a.  If  object  is  more  distant  than  principal  focus,  image  is  real  and 

(1)  enlarged  when  object  is  between  principal  focus  and  twice 
focal  length ; 

(2)  diminished  when  object  is  beyond  two  focal  lengths. 

b.  If  object  is  less  distant  than  principal  focus,  image  is  virtual  and 
always  enlarged. 

3.  Concave  lenses  and  convex  mirrors  have  the  same  optical  prop- 

erties (always  increase  the  curvature  of  the  waves). 
Image  always  virtual  and  diminished  for  any  position  of  object. 


4. 


- 

DO      A     / 


(§  439) 


*  Laboratory  experiments  on  the  formation  of  images  by  concave  mirrors 
and  by  lenses  should  follow  this  discussion.  See,  for  example,  Experiments 
45  and  46  of  the  authors'  Manual. 


IMAGES  IN  MIKKORS  389 

This  formula  may  be  used  in  all  cases  if  the  following  points  are 
borne  in  mind : 

a.  D0  is  always  to  be  taken  as  positive. 

b.  D{  is  to  be  taken  as  positive  for  real  images  and  negative  for 
virtual  images. 

c.  f  is  to  be  taken  as  positive  for  converging  systems  (convex  lenses 
and  concave  mirrors)  and  negative  for  diverging  systems  (con- 
cave lenses  and  convex  mirrors). 

QUESTIONS  AND  PROBLEMS 

1.  Show  from  a  construction  of  the  image  that  a  man  cannot  see 
his  entire  length  in  a  vertical  mirror  unless  the  mirror  is  half  as  tall  as 
he  is.    Decide  from  a  study  of  the  figure  whether  or  not  the  distance  of 
the  man  from  the  mirror  affects  the  case. 

2.  A  man  is  standing  squarely  in  front  of  a  plane  mirror  which  is 
very  much  taller  than  he  is.    The  mirror  is  tipped  toward  him  until 
it  makes  an  angle  of  45°  with  the  horizontal.    He  still  sees  his  full 
length.    What  position  does  his  image  occupy  ? 

3.  How  tall  is  a  tree  200  ft.  away  if  the  image  of  it  formed  by  a 
lens  of  focal  length  4  in.  is  1  in.  long?   (Consider  the  image  to  be  formed 
in  the  focal  plane.) 

4.  How  long  an  image  of  the  same  tree  will  be  formed  in  the  focal 
plane  of  a  lens  having  a  focal  length  of  9  in.? 

5.  What  is  the  difference  between  a  real  and  a  virtual  image? 

6.  When  does  a  convex  lens  form  a  real,  and  when  a  virtual,  image  ? 
When  an  enlarged,  and  when  a  diminished,  image?    When  an  erect, 
and  when  an  inverted,  one  ? 

7.  When  a  camera  is  adjusted  to  photograph  a  distant  object,  what 
change  in  the  length  of  the  bellows  must  be  made  to  photograph  a  near 
object?    Explain  clearly  why  this  adjustment  is  necessary. 

8.  Rays  diverge  from  a  point  20  cm.  in  front  of  a  converging  lens 
whose  focal  length  is  4  cm.    At  what  point  do  the  rays  come  to  a  focus? 

9.  An  object  2  cm.  long  was  placed  10  cm.  from  a  converging  lens 
and  the  image  was  formed  40  cm.  from  the  lens  on  the  other  side.    Find 
the  focal  length  of  the  lens  and  the  length  of  the  image. 

10.  An  object  is  15  cm.  in  front  of  a  convex  lens  of  12  cm.  focal 
length.    What  will  be  the  nature  of  the  image,  its  size,  and  its  distance 
from  the  lens  ? 

11.  Why  does  the  nose  appear  relatively  large  in  comparison  with 
the  ears  when  the  face  is  viewed  in  a  convex  mirror? 

12.  Can  a  convex  mirror  ever  form  an  inverted  image?  Why? 


390 


IMAGE  FORMATION 


FIG.  423.    Image   formed 
small  opening 


by  a 


OPTICAL  INSTRUMENTS 

450.  The  photographic  camera.  A  fairly  distinct,  though  dim, 
image  of  a  candle  flame  can  be  obtained  with  nothing  more 
elaborate  than  a  pinhole  in  a  piece  of  cardboard  (Fig.  423). 
If  the  receiving  screen  is  replaced 
by  a  photographic  plate,  the  ar- 
rangement becomes  a  pinhole 
camera,  with  which  good  pictures 
may  be  taken  if  the  exposure  is 
sufficiently  long.  If  we  try  to 
increase  the  brightness  of  the 
image  by  enlarging  the  hole,  the 
image  becomes  blurred,  because  the  narrow  pencils  a^' ^  <*•$ $ 
etc.  become  cones  whose  bases  a' ^  a'z,  overlap  and  thus  destroy 
the  distinctness  of  the  outline. 

It  is  possible,  without  sacrific- 
ing distinctness  of  outline,  to 
gain  the  increased  brightness  due 
to  the  larger  hole  by  placing 
a  lens  in  the  hole  (Fig.  424). 
If  the  receiving  screen  is  now  a 
sensitive  plate,  the  arrangement 
becomes  a  photographic  camera  (Fig.  425).  But  while  with 
the  pinhole  camera  the  screen  may  be  at  any  distance  from 
the  hole,  with  a  lens  the  plate  and  the 
object  must  be  at  conjugate  foci  of 
the  lens. 

Let  a  lens  of,  say,  4  feet  focal  length 
be  placed  in  front  of  a  hole  in  the  shutter 
of  a  darkened  room,  and  a  semitransparent 
screen  (for  example,  architect's  tracing 
paper)  placed  at  the  focal  plane.  A  per- 
fect reproduction  of  the  opposite  landscape 
will  appear 


FIG.  424.  Principle  of  the  photo- 
graphic camera 


FIG.  425.  The  photographic 
camera 


OPTICAL  INSTRUMENTS 


391 


451.  The  projecting  lantern.  The  projecting  lantern  is  essen- 
tially a  camera  in  which  the  position  of  object  and  image  have 
been  interchanged ;  for  in  the  use  of  the  camera  the  object  is 
at  a  considerable  distance,  and  a  small  inverted  image  is  formed 
on  a  plate  placed  somewhat  farther  from  the  lens  than  the 
focal  distance.  In  the  use  of  the  projecting  lantern  the  object 
P  (Fig.  426)  is  placed  a  trifle  farther  from  the  lens  L1  than 
its  focal  length,  and  an  enlarged  inverted  image  is  formed  on 


Fiu.  426.   The  projecting  lantern  (stereopticon) 

a  distant  screen  S.  In  both  instruments  the  optical  part  is 
simply  a  convex  lens,  or  a  combination  of  lenses  which  is 
equivalent  to  a  convex  lens. 

The  object  P,  whose  image  is  formed  on  the  screen,  is  usu- 
ally a  transparent  slide  which  is  illuminated  by  a  powerful 
light  A.  The  image  is  as  many  times  larger  than  the  object 
as  the  distance  from  L'  to  S  is  greater  than  the  distance  from 
L'  to  P.  The  light  A  is  usually  either  an  incandescent  lamp 
or  an  electric  arc.  The  moving-picture  projector  employs  a 
long  film  of  small  "  positives  "  which  moves  swiftly  between 
the  condensing  lens  L  and  the  projecting  lens  L1  (see  opposite 
p.  386). 

The  above  are  the  only  essential  parts  of  a  projecting  lantern.  In 
order,  however,  that  the  slide  may  be  illuminated  as  brilliantly  as  pos- 
sible, a  so-called  condensing  lens  L  is  always  used.  This  concentrates 
light  upon  the  transparency  and  directs  it  toward  the  screen. 


392 


IMAGE  FORMATION 


In  order  to  illustrate  the  principle  of  the  instrument,  let  a  beam  of 
sunlight  be  reflected  into  the  room  and  fall  upon  a  lantern  slide.  When 
a  lens  is  placed  a  trifle  more  than  its  focal  distance  in  front  of  the  slide, 
a  brilliant  picture  will  be  formed  on  the  opposite  wall. 

452.  The  eye.  The  eye  is  essentially  a  camera  in  which  the 
cornea  C  (Fig.  427),  the  aqueous  humor  I,  and  the  crystalline 
lens  o  act  as  one  single 
lens  which  forms  an 
inverted  image  P'Q'  on 
the  retina,  an  expan- 
sion of  the  optic  nerve 
covering  the  inside  of 
the  back  of  the  eyeball. 

In  the  case  of  the  camera  the  images  of  objects  at  different 
distances  are  obtained  by  placing  the  plate  nearer  to  or  farther 
from  the  lens.  In  the  eye,  however,  the  distance  from  the 
retina  to  the  lens  remains  constant,  and  the  adjustment  for 
different  distances  is  effected  by  changing  the  focal  length 
of  the  lens  system  in  such  a  way  as  always  to  keep  the  image 
upon  the  retina.  Thus,  when  the  normal  eye  is  perfectly 


Q 


FIG.  427.   The  human  eve 


FIG.  428.   The  pupil  dilates  when  the  light  is  dim  and  contracts  when 
it  is  intense 

relaxed,  the  lens  has  just  the  proper  curvature  to  focus  plane 
waves  upon  the  retina,  that  is,  to  make  distant  objects  dis- 
tinctly visible.  But  by  directing  attention  upon  near  objects 
we  cause  the  muscles  which  hold  the  lens  in  place  to  contract 


OPTICAL  INSTRUMENTS 


393 


in  such  a  way  as  to  make  the  lens  more  convex,  and  thus  bring 
into  distinct  focus  objects  which  may  be  as  close  as  eight  or  ten 
inches.  This  power  of  adjustment  or  accommodation,  however, 
varies  greatly  in  different  individuals. 

The  iris,  or  colored  part  of  the  eye,  is  a  diaphragm  which 
varies  the  amount  of  light  which  is  admitted  to  the  retina 
(Figs.  428,  (1)  and  (2)). 

453.  Nearsightedness  and 
farsightedness.  In  a  normal 
eye,  provided  the  lens  is  re- 
laxed and  resting,  parallel  rays 
come  to  a  focus  OR  the  retina 
(Fig.  429,  (1))  ;  in  a  near- 
sighted eye  they  focus  in  front 
of  the  retina  (Fig.  429,  (2))  ; 
and  in  a  far  sighted  eye  they 
reach  the  retina  before  coming 
to  a  focus  (Fig.  429,  (3)). 

Those  who  are  nearsighted 
can  see  distinctly  only  those 
objects  which  are  near.  The 
usual  reason  for  nearsighted- 
ness  is  that  the  retina  is  too 
far  from  the  lens.  The  diverging  lens  corrects  this  defect 
of  vision  because  it  makes  the  rays  from  a  distant  object 
enter  the  eye  as  if  they  had  come  from  an  object  near  by ; 
that  is,  it  partially  counteracts  the  converging  effect  of  the 
eye  (Fig.  429  (2)). 

Those  who  are  farsighted  cannot  when  the  lens  is  relaxed 
see  distinctly  even  a  very  distant  object.  The  usual  reason 
for  farsightedness  is  that  the  eyeball  is  too  short  from  lens  to 
retina.  The  rays  from  near  objects  are  converged,  or  focused, 
towards  f  behind  the  retina  in  spite  of  all  effort  at  accom- 
modation. A  converging  lens  gives  distinct  vision  because 


FIG.  429.    Defects  of  vision 


394 


IMAGE  FORMATION 


it  supplements  the  converging  effect  of  the  eye  (Fig.  429, 
(3)).  In  old  age  the  lens  loses  its  power  of  accommodation, 
that  is,  the  ability  to  become  more  convex  when  looking  at  a 
near  object;  hence,  in  old  age  a  normal  eye  requires  the 
same  sort  of  lens  as  is  used  in  true  farsightedness. 

454.  The  apparent  size  of  a  body.    The  apparent  size  of  a 
body  depends  simply  upon  the  size  of  the  image  formed  upon 
the  retina  by  the  lens  of  the  eye,  and  hence  upon  the  size 
of  the  visual  angle  pCq  (Fig.  430).    The  size  of  this  angle 
evidently  increases  as  the   object  is  brought  nearer  to  the 
eye  (seeP(7$).    Thus,  the  image  formed  on  the  retina  when 
a  man  is  100  feet  from  the  eye  is 

in  reality  only  one  tenth  as  large 

as  the  image  formed  of  the  same 

man  when  he  is  but  10  feet  away. 

We  do  not  actually  interpret  the 

larger    image    as    representing    a 

larger  man  simply  because  we  have 

been  taught  by  lifelong  experience  to  take  account  of  the 

known  distance  of  an  object  in  forming  our  estimate  of  its 

actual  size.    To  an  infant  who  has  not  yet  formed  ideas  of 

distance  the  man  10  feet  away  doubtless  appears  ten  times 

as  large  as  the  man  100  feet  away. 

455.  Distance  of  most  distinct  vision.    When  we  wish  to 
examine  an  object  minutely,  we  bring  it  as  close  to  the  eye  as 
possible  in  order  to  increase  the  size  of  the  image  on  the  retina. 
But  there  is  a  limit  to  the  size  of  the  image  which  can  be  pro- 
duced in  this  way ;  for  when  the  object  is  brought  nearer  to 
the  normal  eye  than  about  10  inches,  the  curvature  of  the 
incident  wave  becomes  so  great  that  the  eye  lens  is  no  longer 
able,  without  too  much  strain,  to  thicken  sufficiently  to  bring 
the  image  into  sharp  focus  upon  the  retina.    Hence  a  person 
with  normal  eyes  holds  an  object  which  he  wishes  to  see  as 
distinctly  as  possible  at  a  distance  of  about  10  inches. 


FIG.  430.   The  visual  angle 


OPTICAL  INSTRUMENTS 


395 


Although  this  so-called  distance  of  most  distinct  vision  varies 
somewhat  with  different  people,  for  the  sake  of  having  a 
standard  of  comparison  in  the  determination  of  the  magnify- 
ing powers  of  optical  instruments  some  exact  distance  had 
to  be  chosen.  The  distance  so  chosen  is  10  inches,  or  25 
centimeters. 

456.  Magnifying  power  of  a  convex  lens.    If  a  convex  lens 
is  placed  immediately  before  the  eye,  the  object  may  be  brought 
much  closer  than  25  centimeters  without  loss  of  distinctness, 
for  the  curvature  of  the 
wave  is  partly  or  even 
wholly  overcome  by  the 
lens  before  the  light  en- 
ters the  eye. 

If  we  wish  to  use  a  lens 
as  a  magnifying  glass  to 
the  best  advantage,  we 
place  the  eye  as  close  to 
it  as  we  can,  so  as  to 
gather  as  large  a  cone  of 
rays  as  possible,  and  then 
place  the  object  at  a  distance  from  the  lens  equal  to  its  focal 
length,  so  that  the  waves  after  passing  through  it  are  plane. 
They  are  then  focused  by  the  eye  with  the  least  possible 
effort.  The  visual  angle  in  such  a  case  is  PcQ  (Fig.  431, (1))  ; 
for,  since  the  emergent  waves  are  plane,  the  rays  which  pass 
through  the  center  of  the  eye  from  P  and  Q  are  parallel  to  the 
lines  through  PC  and  Qc.  But  if  the  lens  were  not  present,  and 
if  the  object  were  25  centimeters  from  the  eye,  the  visual  angle 
would  be  the  small  angle  pcq  (Fig.  431,  (2)).  The  magnify- 
ing power  of  a  simple  lens  is  due,  therefore,  to  the  fact  that 
by  its  use  an  object  can  be  viewed  distinctly  when  held  closer 
to  the  eye  than  is  otherwise  possible.  This  condition  gives  a 
visual  angle  that  increases  the  size  of  the  image  on  the  retina. 


FIG.  431.    Magnifying  power  of  a  lens 


396  IMAGE  FORMATION 

Tl}e  less  the  focal  length  of  the  lens,  the  nearer  to  it  may  the 
object  be  placed,  and  therefore  the  greater  the  visual  angle, 
or  magnifying  power. 

The  ratio  of  the  two  angles  PcQ  and  pcq  is  approximately 
25/f,  where  /  is  the  focal  length  of  the  lens  expressed  in 
centimeters.  Now  the  magnifying  power  of  a  lens  or  microscope 
is  defined  as  the  ratio  of  the  angle  actually  subtended  by  the  image 
when  viewed  through  the  instrument,  to  the  angle  subtended  by  the 
object  when  viewed  with  the  unaided  eye  at  a  distance  of  25  centi- 
meters. Therefore  the  magnifying  power  of  a  simple  lens  is 
25/f.  Thus,  if  a  lens  has  a  focal  length  of  2.5  centimeters,  it 
produces  a  magnification  of  10  diameters  when  the  object  is 
placed  at  its  principal  focus.  If  the  lens  has  a  focal  length 
of  1  centimeter,  its  magnifying  power  is  25,  etc. 

457.  Magnifying  power  of  an  astronomical  telescope.  In  the  astronom- 
ical telescope  the  objective,  or  forward  lens,  forms  at  its  principal  foe  UK  an 
image  P'Q'  of  an  object  PQ  which  is  usually  very  distant.  This  image 


Q 

FIG.  432.   The  magnifying  power  of  a  telescope  objective  is  F/25 

may  be  viewed  by  the  unaided  eye  at  a  distance  of  25  cm.  (Fig.  432). 
The  focal  length  of  the  objective  is  usually  very  much  longer  than  25  cm. 
(about  2000  cm.  in  the  case  of  the  great  Yerkes  telescope  shown  opposite 
p.  365),  so  that  the  visual  angle  P'EQ'  is  increased  by  means  of  the 
objective  alone,  the  increase  being  F/'25*,  that  is,  in  direct  proportion 
to  its  focal  length. 

In  practice,  however,  the  image  is  not  viewed  with  the  unaided  eye, 
but  with  a  simple  magnifying  glass  called  an  eyepiece  (Fig.  433),  placed 
so  that  the  image  is  at  its  focus.  Since  we  have  seen  in  §  456  that  the 
simple  magnifying  glass  increases  the  visual  angle  25// times,  /  being 
the  focal  length  of  the  eyepiece,  it  is  clear  that  the  total  magnification 

*The  angle  PoQ  =  angle  P'oQf.  Consider  the  short  line  Q'P'  as  an  arc, 
and  the  angles  Q'EP'  and  Q'oP'  are  inversely  proportional  to  their  radii, 
F  and  25. 


OPTICAL  INSTRUMENTS 


397 


produced  by  both  lenses,  used  as  above,  is  F/25  x  25/f=F/f,  The. 
magnifying  power  of  an  astronomical  telescope  is  therefore  the  focal  length  of 
the  objective  divided  by  the  focal  length  of  the  eyepiece.  It  will  be  seen, 
therefore,  that  to 
get  a  high  mag- 
nifying power 
it  is  necessary  Objective  ^-\^  Eye- 

to  use  an  objec-    Top-  MIMllliniinnn, ^Plfcel 

tive  of  as  great  To  Q 
focal  length  as 
possible  and  an 
eyepiece  of  as 
short  focal  length 
as  possible.  The 
focal  length  of 


FIG.  433.   The  magnifying  power  of  a  telescope  is  F/f 


eyepiece 


the  great  lens  at  the  Yerkes  Observatory  is  about  C2  feet,  and  its  diam- 
eter 40  inches.  The  great  diameter  enables  it  to  collect  a  very  large 
amount  of  light,  which  makes  celestial  objects  more  plainly  visible. 

Eyepieces  often  have  focal  lengths  as  small  as  -|  inch.  Thus,  the 
Yerkes  telescope,  when  used  with  a  ^-inch  eyepiece,  has  a  magnifying 
power  of  2976. 

458.  The  magnifying  power  of  the  com- 
pound microscope.  The  compound  micro- 
scope is  like  the  telescope  in  that  the 
front  lens,  or  objective,  forms  a  real  image 
of  the  object  at  the  focus  of  the  eyepiece. 
The  size  of  the  image  P'Q'  (Fig.  434) 
formed  by  the  objective  is" as  many  times 
the  size  of  the  object  PQ  as  vf  the  dis- 
tance from  the  objective  to  the  image, 
is  times  u,  the  distance  from  the  objec- 
tive to  the  object  (see  §  441).  Since  the 
eyepiece  magnifies  this  image  25// times, 
the  total  magnifying  power  of  a  com- 


,      .            .     .    t-25 
pound  microscope  is 


Ordinarily  v 


FIG.  434.   The  compound 
microscope 


is  practically  the  length  L  of  the  micro- 
scope tube,  and  u  is  the  focal  length  F  of  the  objective.    Wherever 
this  is  the  case,  then,  the  magnifying  power  of  the  compound  micro- 

.    25  L 
scope  is-— 


398  IMAGE  FORMATION 

The  relation  shows  that  in  order  to  get  a  high  magnifying  power  with 
a  compound  microscope  the  focal  length  of  both  eyepiece  and  objective 
should  be  as  short  as  possible,  while  the  tube  length  should  be  as  long 
as  possible.  Thus,  if  a  microscope  has  both  an  eyepiece  and  an  objective 
of  6  millimeters  focal  length  and  a  tube  15  centimeters  long,  its  magni- 
fying power  will  be  — —  =  1042.  Magnifications  as  high  as  2500  or 

.5  x  .0 

3000  are  sometimes  used,  but  it  is  impossible  to  go  much  farther,  for  the 
reason  that  the  image  becomes  too  faint  to  be  seen  when  it  is  spread 
over  so  large  an  area. 

459.  The  opera  glass.  On  account  of  the  large  number  of  lenses 
which  must  be  used  in  the  terrestrial  telescope,  it  is  too  bulky  and  awk- 
ward for  many  purposes,  and  hence  it  is  often  replaced  by  the  opera 
glass  (Fig.  435).  This  instrument  consists  of  an  objective  like  that  of 


FIG.  435.    The  opera  glass 

the  telescope,  and  an  eyepiece  which  is  a  concave  lens  of  the  same  focal 
length  as  the  eye  of  the  observer.  The  effect  of  the  eyepiece  is  there- 
fore to  just  neutralize  the  lens  of  the  eye.  Hence  the  objective,  in  effect, 
forms  its  image  directly  upon  the  retina.  It  will  be  seen  that  the  size 
of  the  image  formed  upon  the  retina  by  the  objective  of  the  opera  glass 
is  as  much  greater  than  the  size  of  the  image  formed  by  the  naked  eye 
as  the  focal  length  CR  of  the  objective  is  greater  than  the  focal  length 
cR  of  the  eye.  Since  the  focal  length  of  the  eye  is  the  same  as  that  of 
the  eyepiece,  the  magnifying  power  of  the  opera  glass,  like  that  of  the  astro- 
nomical telescope,  is  the  ratio  of  the  focal  lengths  of  the  objective  and  eyepiece. 
Objects  seen  with  an  opera  glass  appear  erect,  since  the  image  formed 
on  the  retina  is  inverted,  as  is  the  case  with  images  formed  by  the  lens 
of  the  eye  unaided. 

460.  The  stereoscope.  Binocular  vision.  When  an  object  is  seen  with 
both  eyes,  the  images  formed  on  the  two  retinas  differ  slightly,  because 
of  the  fact  that  the  two  eyes,  on  account  of  their  lateral  separation,  are 
viewing  the  object  from  slightly  different  angles.  It  is  this  difference 


OPTICAL  INSTRUMENTS 


399 


in  the  two  images  which  gives  to  an  object  or  landscape  viewed  with 
two  eyes  an  appearance  of  depth,  or  solidity,  which  is  wholly  wanting 
when  one  eye  is  closed.  The  stereoscope  is  an  in- 
strument which  reproduces  in  photographs  this 
effect  of  binocular  vision.  Two  photographs  of  the 
same  object  are  taken  from  slightly  different  points 
of  view.  These  photographs  are  mounted  at  A  and 
B  (Fig.  436),  where  they  are  simultaneously  viewed 
by  the  two  eyes  through  the  two  prismatic  lenses  m 
and  n.  These  two  lenses  superpose  the  two  images 
at  C  because  of  their  action  as  prisms,  and  at  the 
same  time  magnify  them  because  of  their  action  as 
simple  magnifying  lenses.  The  result  is  that  the 
observer  is  conscious  of  viewing  but  one  photograph ; 
but  this  differs  from  ordinary  photographs  in  that,  FIG.  436.  Principle 
instead  of  being  flat,  it  has  all  of  the  characteristics  of  the  stereoscope 
of  an  object  actually  seen  with  both  eyes. 

The  opera  glass  has  the  advantage  over  the  terrestrial  telescope  of 
affording  the  benefit  of  binocular  vision  ;  for  while  telescopes  are  usually 
constructed  with  one  tube,  opera  glasses  always  have  two,  one  for  each  eye. 

461.  The  Zeiss  binocular.  The  greatest  disadvantage  of  the  opera 
glass  is  that  the  field  of  view  is  very  small.  The  terrestrial  telescope 
has  a  larger  field  but  is  of  inconvenient  length.  An  instrument  called 
the  Zeiss  binocular  (Fig.  437) 
has  recently  come  into  use, 
which  combines  the  compact- 
ness of  the  opera  glass  with  the 
wide  field  of  view  of  the  ter- 
restrial telescope.  The  compact- 
ness is  gained  by  causing  the 
light  to  pass  back  and  forth 
through  total  reflecting  prisms, 
as  in  the  figure.  These  reflec- 
tions also  perform  the  function 
of  reinverting  the  image,  so 
that  the  real  image  which  is 
formed  at  the  focus  of  the  eye- 
piece is  erect.  It  will  be  seen,  therefore,  that  the  instrument  is  essen- 
tially an  astronomical  telescope  in  which  the  image  is  reinverted  by 
reflection,  and  in  which  the  tube  is  shortened  by  letting  the  light  pass 
back  and  forth  between  the  prisms. 


FIG.  437.   The  Zeiss  binocular 


400 


IMAGE  FORMATION 


A  further  advantage  which  is  gained  by  the  Zeiss  binocular  is  due  to 
the  fact  that  the  two  objectives  are  separated  by  a  distance  which  is 
greater  than  the  distance  between  the  eyes,  so  that  the  stereoscopic 
effect  is  more  prominent  than  with  the  unaided  eye  or  with  the  ordinary 
opera  glass.* 

462.  The  periscope.  A  periscope  is  a  sort  of  double-jointed  telescope 
which  makes  use  of  total  reflection  twice,  —  at  the  top  and  at  the  bottom. 
The  system  of  lenses  gives  a  magnification  of  about  1^  diameters,  as 


FIG.  438.   A  parabolic  reflector 

this  has  been  found  best  to  make  ships  appear  at  their  true  distances 
from  the  submarine.  There  is  no  stereoscopic  effect,  since  the  periscope 
is  not  double  like  a  binocular. 

463.  Parabolic  reflectors.  For  the  projection  of  a  more  nearly  cylin- 
drical beam  than  is  possible  with  spherical  mirrors,  it  is  customary  to 
use  parabolic  reflectors,  as  in  automobile  headlights  (Fig.  438,  (1)  and 
(2)).  The  light  is  placed  a  little  closer  to  the  reflector  than  the  princi- 
pal focus,  so  that  the  reflected  light  may  spread  somewhat.  The  same 
principle  is  employed  in  searchlights,  except  that  the  source  of  light 
(usually  a  powerful  arc)  is  kept  more  nearly  at  the  principal  focus  of 
the  reflector.  The  Sperry  60-inch  searchlight,  the  most  powerful  in  the 
world,  has  a  beam  candle  power  of  approximately  two  thirds  that  of  the 
sun,  and  its  light  is  plainly  visible  at  a  distance  of  one  hundred  miles. 

*  Laboratory  experiments  on  the  magnifying  powers  of  lenses  and  on  the 
construction  of  microscopes  and  telescopes  should  follow  this  chapter.  See 
for  example,  Experiments  47,  48,  and  49  of  the  authors'  Manual. 


OPTICAL  INSTRUMENTS  401 

QUESTIONS  AND  PROBLEMS 

1.  Why  is  it  necessary  for  the  pupils  of  your  eyes  to  be  larger  in  a 
dim  cellar  than  in  the  sunshine?    Why  does  the  photographer  use  a 
large  stop  on  dull  days  in  photographing  moving  objects  ? 

2.  If  a  photographer  wishes  to  obtain  the  full  figure  on  a  plate  of 
cabinet  size,  does  he  place  the  subject  nearer  to  or  farther  from  the 
camera  than  if  he  wishes  to  take  the  head  only?    Why? 

3.  A  child  3  ft.  in  height  stood  15  ft.  from  a  camera  whose  lens  had 
a  focal  length  of  18  in.    What  was  the  distance  from  the  lens  to  the 
photographic  plate  and  the  length  of  the  child's  photograph? 

4.  If  20  sec.  is  the  proper  length  of  exposure  when  you  are  printing 
photographs  by  a  gas  light  8  in.  from  the  printing  frame,  what  length 
of  exposure  would  be  required  in  printing  from  the  same  negative  at 
a  distance  of  16  in.  from  the  same  light? 

5.  If  a  20-second  exposure  is  correct  at  a  distance  of  6  in.  from  an 
8-candle-power  electric  light,  wThat  is  the  required  time  of  exposure 
at  a  distance  of  12  in.  from  a  32-candle-power  electric  light? 

6.  The  image,  on  the  retina,  of  a  book  held  a  foot  from  the  eye  is 
larger  than  that  of  a  house  on  the  opposite  side  of  the  street.    Why  do 
we  not  judge  that  the  book  is  actually  larger  than  the  house? 

7.  W^hat  sort  of  lenses  are  necessary  to  correct  shortsightedness? 
longsightedness?   Explain  with  the  aid  of  a  diagram. 

8.  What  is  the  magnifying  power  of  a  J-in.  lens  used  as  a  simple 
magnifier? 

9.  If  the  length  of  a  microscope  tube  is  increased  after  an  object 
has  been  brought  into  focus,  must  the  object  be  moved  nearer  to  or 
farther  from  the  lens  in  order  that  the  image  may  again  be  in  focus  ? 

10.  Explain  as  well  as  you  can  how  a  telescope  forms  the  image 
that  you  see  when  you  look  into  it. 

11.  Is  the  image  on  the  retina  erect  or  inverted? 


CHAPTER  XX 


COLOR  PHENOMENA 
COLOR  AND  WAVE  LENGTH 
464.  Wave  lengths  of  different  colors.   Let  a  soap  film  be  formed 

across  the  top  of  an  ordinary  drinking  glass,  care  being  taken  that  both 

the  solution  and  the  glass  are  as  clean  as  possible.    Let  a  beam  of  sun- 

light or  the  light  from  a  projecting  lantern  pass  through  a  piece  of  red 

glass  at  A,  fall  upon  the  soap  film  F,  and  be  reflected  from  it  to  a  white 

screen  S  (see  Fig.  439).    Let 

a  convex  lens  L  of  from  6 

to  12  inches  focal  length  be 

placed  in  the  path  of  the  re- 

flected beam  in  such  a  posi- 

tion as  to  produce  an  image 

of  the  film  upon  the  screen 

S,  that  is,  in  such  a  position 

that  film  and  screen  are  at 

conjugate  foci  of  the  lens. 

The  system  of  red  and  black 

bands    upon    the    screen    is 

formed  precisely  as  in  §  427, 

by  the  interference   of  the 

two  beams  of  light  coming 

from  the  front  and  back  sur- 


FIG. 439.    Projection  of  soap-film  fringes 


faces  of  the  wedge-shaped 
film.  Now  let  the  red  glass 
be  held  in  one  half  of  the  beam  and  a  piece  of  green  glass  in  the  other 
half,  the  two  pieces  being  placed  edge  to  edge,  as  shown  at  A.  Two 
sets  of  fringes  will  be  seen  side  by  side  on  the  screen.  The  fringes  will 
be  red  and  black  on  one  side  of  the  image,  and  green  and  black  on  the 
other  ;  but  it  will  be  noticed  at  once  that  the  dark  bands  on  the  green 
side  are  closer  together  than  the  dark  bands  on  the  other  side  ;  in 

402 


COLOR  AND  WAVE  LENGTH 


403 


fact,  seven  fringes  on  the  side  of  the  film  which  is  covered  by  the 
green  glass  will  be  seen  to  cover  about  the  same  distance  as  six  fringes 
on  the  red  side.* 

Since  it  was  shown  in  Fig.  390  that  the  distance  between 
two  dark  bands  corresponds  to  an  increase  of  one-half  wave 
length  in  the  thickness  of  the  film,  we  conclude,  from  the  fact 
that  the  dark  bands  on  the  red  side  are  farther  apart  than  those 
on  the  green  side,  that  red  light  must  have  a  longer  wave  length 
than  green  light.  The  wave  length  of  the  central  portion  of 
each  colored  region  of  the  spectrum  is  roughly  as  follows : 

Red.     .     .     ...     .000068cm.         Green     .     .     .     .000052cm. 

Yellow  .     .     .     .     .     .000058cm.         Blue 000046cm. 

Violet 000042cm. 

Let  the  red  and  green  glasses  be  removed  from  the  path  of  the  beam. 
The  red  and  green  fringes  will  be  seen  to  be  replaced  by  a  series  of 
bands  brilliantly  colored  in  different  hues.    These  are  due  to  the  fact 
that  the  lights  of  different  wave  length 
form   interference   bands  at  different 
places  on  the  screen.    Notice  that  the 
upper  edges  of  the  bands  (lower  edges 
in  the   inverted  image)    are    reddish, 
while  the  lower  edges  are  bluish.    We 
shall  find  the  explanation  of  this  fact 
in  §  473. 

465.  Composite  nature  of  white 
light.  Let  a  beam  of  sunlight  pass 
through  a  narrow  slit  and  fall  on  a 
prism,  as  in  Fig.  440.  The  beam  which 
enters  the  prism  as  white  light  is 

dispersed  into  red,  yellow,  green,  blue,  and  violet  lights,  although  each 
color  merges,  by  insensible  gradations,  into  the  next.  This  band  of 
color  is  called  a  spectrum. 

We  conclude  from  this  experiment  that  white  light  is  a  mix- 
ture of  all  the  colors  of  the  spectrum,  from  red  to  violet  inclusive. 


FIG.  440.    White  light  decom- 
posed by  a  prism 


*  The  experiment  may  be  performed  at  home  by  simply  looking  through 
red  and  green  glasses  at  a  soap  film  so  placed  as  to  reflect  white  light  to  the  eye. 


404  COLOR  PHENOMENA 

466.  Color  of  bodies  in  white  light.     Let  a  piece  of  red  glass  be 
held  in  the  path  of  the  colored  beam  of  light  in  the  experiment  of  the 
preceding  section.    All  the  spectrum  except  the  red  will  disappear,  thus 
showing  that  all  the  wave  lengths  except  red  have  been  absorbed  by  the 
glass.    Let  a  green  glass  be  inserted  in  the  same  way.    The  green  portion 
of  the  spectrum  will  remain  strong,  while  the  other  portions  will  be 
greatly  enfeebled.     Hence  green  glass  must  have  a  much  less  absorbing 
effect  upon  wave  lengths  which  correspond  to  green  than  upon  those 
which  correspond  to  red  and  blue.   Let  the  green  and  red  glasses  be  held 
one  behind  the  other  in  the  path  of  the  beam.    The  spectrum  will  almost 
completely  vanish,  for  the  red  glass  has  absorbed  all  except  the  red  rays, 
and  the  green  glass  has  absorbed  these. 

We  conclude,  therefore,  that  the  color  wHich  a  body  has  in 
ordinary  daylight  is  determined  by  the  wave  lengths  which 
the  body  has  not  the  power  of  absorbing.  Thus,  if  a  body 
appears  white  in  daylight,  it  is  because  it  diffuses  or  reflects 
all  wave  lengths  equally  to  the  eye,  and  does  not  absorb  one 
set  more  than  another.  For  this  reason  the  light  which  comes 
from  it  to  the  eye  is  of  the  same  composition  as  daylight  or 
sunlight.  If,  however,  a  body  appears  red  in  daylight,  it  is 
because  it  absorbs  the  red  rays  of  the  white  light  which  falls 
upon  it  less  than  it  absorbs  the  others,  so  that  the  light  which 
is  diffusely  reflected  contains  a  larger  proportion  of  red  wave 
lengths  than  is  contained  in  ordinary  light.  Similarly,  a  body 
appears  yellow,  green,  or  blue  when,  it  absorbs  less  of  one  of 
these  colors  than  of  the  rest  of  the  colors  contained  in  white 
light,  and  therefore  sends  a  preponderance  of  some  particular 
wave  length  to  the  eye. 

467.  Color  of  bodies  placed  in  colored  lights.    Let  a  body  which 

appears  wThite  in  sunlight  be  placed  in  the  red  end  of  the  spectrum.  It 
will  appear  to  be  red.  In  the  blue  end  of  the  spectrum  it  will  appear  to 
be  blue,  etc.  This  confirms  the  conclusion  of  the  last  paragraph,  that 
a  white  body  has  the  power  of  diffusely  reflecting  all  the  colors  of  the 
spectrum  equally. 

Next  let  a  skein  of  red  yarn  be  held  in  the  blue  end  of  the  spec- 
trum. It  will  appear  nearly  black.  In  the  red  end  of  the  spectrum 


COLOR  AND  WAVE  LENGTH 


405 


it  will  appear  strongly  red.  Similarly,  a  skein  of  blue  yarn  will  appear 
nearly  black  in  all  the  colors  of  the  spectrum  except  blue,  where  it 
will  have  its  proper  color. 

These  effects  are  evidently  due  to  the  fact  that  the  red  yarn, 
for  example,  has  the  power  of  diffusely  reflecting  red  wave 
lengths  copiously,  but  of  absorbing,  to  a  large  extent,  the  others. 
Hence,  when  held  in  the  blue  end  of  the  spectrum,  it  sends 
but  little  color  to  the  eye,  since  no  red  light  is  falling  upon  it. 

Soak  a  handful  of  asbestos  or  cotton  batting  in  a  saturated  salt  solu- 
tion ;  squeeze  out  most  of  the  brine ;  pour  over  the  material  a  quantity 
of  strong  alcohol.  When  ignited,  this  will  produce  a  large  flame  of  al- 
most pure-yellow  light.  In  a  darkened  room  allow  the  yellow  light  to 
fall  strongly  upon  a  spectrum  chart  of  six  colors.  The  only  color  on  the 
chart  that  appears  natural  is  the  yellow. 

468.  Compound  colors.  It  must  not  be  inferred  from  the 
preceding  paragraphs  that  every  color  except  white  has  one 
definite  wave  length,  for  the  same  effect 
may  be  produced  on  the  eye  by  a  mix- 
ture of  several  different  wave  lengths 
as  is  produced  by  a  single  wave  length. 
This  statement  may  be  proved  by  the 
use  of  an  apparatus  known  as  Newton's 
color  disk  (Fig.  441).  The  arrangement 
makes  it  possible  to  rotate  differently 
colored  sectors  so  rapidly  before  the  eye 
that  the  effect  is  precisely  the  same  as 
though  the  colors  came  to  the  eye  simul- 
taneously. If  one  half  of  the  disk  is 
red  and  the  other  half  green,  the  rotat- 
ing disk  will  appear  yellow,  the  color 
being  very  similar  to  the  yellow  of  the 
spectrum.  If  green  and  violet  are  mixed 
in  the  same  way,  the  result  will  be  light  blue.  Although  the 
colors  produced  in  this  way  are  not  distinguishable  by  the  eye 


FIG.  441.    Newton's 
color  disk 


406  COLOK  PHENOMENA 

from  spectral  colors,  it  is  obvious  that  their  physical  constitu- 
tion is  wholly  different ;  for  while  a  spectral  color  consists  of 
waves  of  a  single  wave  length,  the  colors  produced  by  mix- 
ture are  compounds  of  several  wave  lengths.  For  this  reason 
the  spectral  colors  are  called  pure  and  the  others  compound. 
In  order  to  tell  whether  the  color  of  an  object  is  pure  or  com- 
pound, it  is  only  necessary  to  observe  it  through  a  prism.  If 
it  is  compound,  the  colors  will  be  separated,  giving  an  image 
of  the  object  for  each  color.  If  it  is  pure,  the  object  will  appear 
through  the  prism  exactly  as  it  does  without  the  prism. 

By  compounding  colors  in  the  way  described  above  we 
can  produce  many  which  are  not  found  in  the  spectrum. 
Thus,  mixtures  of  red  and  blue  give  purple  or  crimson ; 
mixtures  of  black  with  red,  orange,  or  yellow  give  rise  to 
the  various  shades  of  brown.  Lavender  may  be  formed  by 
adding  three  parts  of  white  to  one  of  blue ;  lilac,  by  adding 
to  fifteen  parts  of  white  four  parts  of  red  and  one  of  blue ; 
olive,  by  adding  one  part  of  black  to  two  parts  of  green  and 
one  of  red. 

469.  Complementary  colors.  Since  white  light  is  a  combi- 
nation of  all  the  colors  from  red  to  violet  inclusive,  it  might 
be  expected  that  if  one 

or  several  of  these  colors  L 

were      subtracted      from  a       frrTrrrrl0fi(^  . 

white   light,    the  residue 
would  be   colored   light. 

To  test  this  experimentally 
let   a   beam   of    sunlight  be 
passed    through   a    slit   s,   a 
prism  P,  and  a  lens  L,  to  a     rIG<442.  Recombination  of  spectral  colors 
screen     S,    arranged     as    in  into  white  light 

Fig.  442.  A  spectrum  will  be 

formed  at  R  V,  the  position  conjugate  to  the  slit  s,  and  a  pure  white 
spot  will  appear  on  the  screen  when  it  is  at  the  position  which  is  conju- 
gate to  the  prism  face  ab.  Let  a  card  be  slipped  into  the  path  of  the 


COLOR  AND  WAVE  LENGTH  407 

beam  at  E,  so  as  to  cut  off  the  red  portion  of  the  light.  The  spot  on  S 
will  appear  a  brilliant  shade  of  greenish  blue.  This  is  the  compound 
color  left  after  red  is  taken  from  the  white  light.  This  shade  of  blue 
is  therefore  called  the  complementary  color  of  the  red  which  has  been 
subtracted.  Two  complementary  colors  are  therefore  denned  as  any  two 
colors  which  produce  white  when  added  to  each  other. 

Let  the  card  be  slipped  in  from  the  side  of  the  blue  rays  at  V.  The 
spot  will  first  take  on  a  yellowish  tint  when  the  violet  alone  is  cut  out; 
and  as  the  card  is  slipped  farther  in,  the  image  will  become  a  deep  shade 
of  red  when  violet,  blue,  and  part  of  the  green  are  cut  out. 

Next  let  a  lead  pencil  be  held  vertically  between  R  and  V  so  as  to 
cut  off  the  middle  part  of  the  spectrum ;  that  is,  the  yellow  and  green 
rays.  The  remaining  red,  blue,  and  violet  will  unite  to  form  a  brilliant 
purple.  In  each  case  the  color  on  the  screen  is  the  complement  of  that 
which  is  cut  out. 

470.  Retinal  fatigue.    Let  the  gaze  be  fixed  intently  for  not  less 
than  twenty  or  thirty  seconds  on  a  point  at  the  center  of  a  block  of  any 
brilliant  color  —  for  example,  red.    Then  look  off  at  a  dot  on  a  white 
wall  or  a  piece  of  white  paper,  and  hold  the  gaze  fixed  there  for  a  few 
seconds.    The  brilliantly  colored  block  will  appear  on  the  white  wall, 
but  its  color  will  be  the  complement  of  that  first  looked  at. 

The  explanation  of  this  phenomenon,  due  to  so-called  "  ret- 
inal fatigue,"  is  found  in  the  fact  that  although  the  white  sur- 
face is  sending  waves  of  all  colors  to  the  eye,  the  nerves  which 
responded  to  the  color  first  looked  at  have  become  fatigued, 
and  hence  fail  to  respond  to  this  color  when  it  comes  from  the 
white  surface.  Therefore  the  sensation  produced  is  that  due 
to  white  light  minus  this  color ;  that  is,  to  the  complement  of 
the  original  color.  A  study  of  the  spectral  colors  by  this 
method  shows  that  the  following  colors  are  complementary. 

Red  Orange  Yellow       Violet  Green 

Bluish  green       Greenish  blue      Blue  Greenish  yellow       Crimson 

471.  Color  of  pigments.    When  yellow  light  is  added  to  the 
proper  shade  of  blue,  white  light  is  produced,  since  these 
colors  are  complementary.    But  if  a  yellow  pigment  is  added 
to  a  blue  one,  the  color  of  the  mixture  will  be  green.    This  is 


408  COLOR  PHENOMENA 

because  the  yellow  pigment  removes  the  blue  and  violet  by 
absorption,  and  the  blue  pigment  removes  the  red  and  yellow, 
so  that  only  green  is  left. 

When  pigments  are  mixed,  therefore,  each  one  subtracts  cer- 
tain colors  from  white  light,  and  the  color  of  the  mixture  is  that 
color  which  escapes  absorption  by  the  different  ingredients. 
Adding  pigments  and  adding  colors,  as  in  §  468,  are  therefore 
wholly  dissimilar  processes  and  produce  widely  different  results. 

472.  Three-color  printing.    It  is  found  that  all  colors  can  be 
produced  by  suitably  mixing  with  the  color  disk  (Fig.  441) 
three    spectral    colors,   namely   red,    green,   and   blue-violet. 
These  are  therefore  called  the  three  primary  colors.    The  so- 
called  primary  pigments  are  simply  the  complements  of  these 
three  primary  colors.    They  are,  in  order,  peacock  blue,  crim- 
son, and  light  yellow.    The  three  primary  colors  when  mixed 
yield  white.    The  three  primary  pigments  when  mixed  yield 
black,  because  together  they  subtract  all  the  ingredients  from 
white  light.    The  process  of  three-color  printing  consists  in 
mixing  on  a  white  background,  that  is,  on  white  paper,  the 
three  primary  pigments  in  the  following  way:  Three  differ- 
ent photographs  of  a  given-colored   object  are  taken,  each 
through  a  filter  of  gelatin  stained  the  color  of  one  of  the 
primary  colors.    From  these  photographs  halftone  "  blocks  " 
are  made  in  the  usual  way.    The  colored  picture  is  then  made 
by  carefully  superposing  prints  from  these  blocks,  using  with 
each  an  ink  whose  color  is  the  complement  of  that  of  the 
"  filter  "  through  which  the  original  negative  was  taken.    The 
plate  on  the  opposite  page  illustrates  fully  the  process.   It  will 
be  interesting  to  examine  differently  colored  portions  with  a 
lens  of  moderate  magnifying  power. 

473.  Colors  of  thin  films.   The  study  of  complementary  colors 
has  furnished  us  with  the  key  to  the  explanation  of  the  fact, 
observed  in  §  464,  that  the  upper  edge  of  each  colored  band 
produced  by  the  water  wedge  is  reddish,  while  the  lower  edge 


THREE-COLOR  PRINTING 

1,  yellow  impression  (negative  made  through  a  blue-violet  filter) ;  2,  crimson  im- 
pression (negative  made  through  a  green  filter) ;  3,  crimson  on  yellow ;  4,  blue 
impression  (negative  made  through  a  red  filter) ;  5,  yellow,  crimson,  and  blue 
combined  (the  final  product).  The  circles  at  the  right  show  the  colors  of  ink  used 
in  making  each  impression.  Notice  the  different  colors  in  5,  which  are  made  by 
combining  yellow,  crimson,  and  blue 


COLOE  AND  WAVE  LENGTH 


409 


is  bluish.  The  red  on  the  upper  edge  is  due  to  the  fact  that 
there  the  shorter  blue  waves  are  destroyed  by  interference  and 
a  complementary  red  color  is  left;  while  on  the  lower  edge 
of  each  fringe,  where  the  film  is  thicker,  the  longer  red  waves 
interfere,  leaving  a  complementary  blue.  In  fact,  each  wave 
length  of  the  incident  light  produces  a  set  of  fringes,  and  it  is 
the  superposition  of  these  different  sets  which  gives  the  result- 
ant colored  fringes.  Where  the  film  is  too  thick  the  overlapping 
is  so  complete  that  the  eye  is  unable  to  detect  any  trace  of 
color  in  the  reflected  light. 

In  films  which  are  of  uniform  thickness,  instead  of  wedge- 
shaped,  the  color  is  also  uniform,  so  long  as  the  observer  does 
not  change  the  angle  at  which  the  film  is  viewed.  With  any 
change  in  this  angle  the  thickness  of  film  through  which  the 
light  must  pass  in  coming  to  the  observer  changes  also,  and 
hence  the  color  changes.  This  explains  the  beautiful  play  of 
iridescent  colors  seen  in  soap  bubbles,  thin  oil  films,  mother 
of  pearl,  etc. 

474.  Chromatic  aberration.  It  has  heretofore  been  assumed 
that  all  the  waves  which  fall  on  a  lens  from  a  given  source 
are  brought  to  one  and  the 
same  focus.  But  since  blue 
rays  are  bent  more  than  red 
ones  in  passing  through  a 
prism,  it  is  clear  that  in 
passing  through  a  lens  the 

blue  light  must  be  brought  to  a  focus  at  some  point  v  (Fig.  443) 
nearer  to  the  lens  than  r,  where  the  red  light  is  focused,  and 
that  the  foci  for  intermediate  colors  must  fall  in  intermediate 
positions.  It  is  for  this  reason  that  an  image  formed  by  a 
simple  lens  is  always  fringed  with  color. 

Let  a  card  be  held  at  the  focus  of  a  lens  placed  in  a  beam  of  sunlight 
(Fig.  443).  If  the  card  is  slightly  nearer  the  lens  than  the  focus,  the 
spot  of  light  will  be  surrounded  by  a  red  fringe,  for  the  red  rays,  being 


FIG.  443.  Chromatic  aberration  in  a  lens 


410  COLOB,  PHENOMENA 

least  refracted,  are  on  the  outside.  If  the  card  is  moved  out  beyond  the 
focus,  the  red  fringe  will  be  found  to  be  replaced  by  a  blue  one ;  for 
after  crossing  at  the  focus  it  will  be  the  more  refrangible  rays  which 
will  then  be  found  outside. 

This  dispersion  of  light  produced  by  a  lens  is  called  chromatic 
aberration. 

475.  Achromatic  lenses.    The  color  effect  caused  by  the 
chromatic  aberration  of  a  simple  lens  greatly  impairs  its  use- 
fulness.   Fortunately,  however,  it  has  been  found  possible  to 
eliminate  this  effect  almost  completely  by 
combining  into  one  lens  a  convex  lens  of 
crown   glass   and   a  concave   lens  of  flint 
glass  (Fig.  444).    The  first  lens  then  pro- 
duces  both  bending  and  dispersion,  while 

FIG.  444.  An  achro- 

the  second  almost   completely   overcomes  maticlens 

the  dispersion  without  entirely  overcoming 
the  bending.  Such  lenses  are  called  achromatic  lenses.  The  first 
one  was  made  by  John  Dollond  in  London  in  1758.   They  are 
used  in  the  construction  of  all  good  telescopes  and  microscopes. 

QUESTIONS  AND  PROBLEMS 

1.  What  determines  the  color  of  an  opaque  body?    a  transparent 
body?    What  is  the  appearance  of  a  bunch  of  green  grass  when  seen 
by  pure  red  light?    Explain. 

2.  What  is  w  white  "  ?  What  is  "  black  "  ?  Explain  why  a  block  of  ice 
is  transparent  while  snow  is  opaque  and  white. 

3.  Why  do  white  bodies  look  blue  when  seen  through  a  blue  glass  ? 

4.  What  color  would  a  yellow  object  appear  to  have  if  looked  at 
through  a  blue  glass?    (Assume  that  the  yellow  is  a  pure  color.) 

5.  A  gas  flame  is  distinctly  yellow  as  compared  with  sunlight.  What 
wave  lengths,  then,  must  be  comparatively  weak  in  the  spectrum  of  a 
gas  flame  ? 

6.  Why  does  dark  blue  appear  black  by  candle  light? 

7.  Certain  blues  and  greens  cannot  be  distinguished  from  each  other 
by  candle  light.    Explain. 

8.  Does  blue  light  travel  more  slowly  or  faster  in  glass  than  red  light  ? 
How  do  you  know? 


SPECTRA 


411 


SPECTRA 

476.  The  rainbow.  There  is  formed  in  nature  a  very  beau- 
tiful spectrum  with  which  everyone  is  familiar  —  the  rainbow. 

Let  a  spherical  bulb  F  (Fig.  445)  1J  or  2  inches  in  diameter  be  filled 
with  water  and  held  in  the  path  of  a  beam  of  sunlight  which  enters  the 
room  through  a  hole  in  a  piece  of  cardboard  AB.    A  miniature  rainbow 
will    be    formed    on   the 
screen  around  the   open- 
ing,  the  violet  edge  of  the 
bow  being  toward  the  cen- 
ter of  the  circle  and  the 
red  outside.    A  beam  of 
light    which    enters    the 
flask  at  C  is  there  both 
refracted   and    dispersed ; 
at  D  it  is  totally  reflected  ; 
and  at  E  it  is  again  re- 
fracted and  dispersed  on 
passing  out  into  the  air. 
Since  in  both  of  the  re- 
fractions the  violet  is  bent  more  than  the  red,  it  is  obvious  that  it  must 
return  nearer  to  the  direction  of  the  incident  beam  than  the  red  rays. 
If  the  flask  were  a  perfect  sphere,  the  angle  included  between  the  inci- 
dent ray  OC  and  the  emergent  red  ray  ER  would  be  42° ;  and  the  angle 
between  the  incident  ray  and  the  emergent  violet  ray  E  V  would  be  40°. 

The  actual  rainbow  seen  in  the  heavens  is  due  to  the 
refraction  and  reflection  of  light  in  the  drops  of  water  in 
the  air,  which  act  exactly  as  did  the  flask  in  the  preceding 
experiment.  If  the  observer  is  standing  at  E  with  his  back 
to  the  sun,  the  light  which  comes  from  the  drops  so  as  to 
make  an  angle  of  42°  (Fig.  446)  with  the  line  drawn  from 
the  observer  to  the  sun  must  be  red  light ;  while  the  light 
which  comes  from  drops  which  are  at  an  angle  of  40°  from 
the  eye  must  be  violet  light.  In  direct  sunshine  the  pris- 
matic color  seen  in  a  dewdrop  changes  to  another  color  when 
the  head  is  shifted  side  wise.  It  is  clear  that  those  drops 


FIG.  445.    Artificial  rainbow 


412 


COLOR  PHENOMENA 


Sal» 


whose  direction  from  the  eye  makes  any  particular  angle 
with  the  line  drawn  from  the  eye  to  the  sun  must  lie  on  a 
circle  whose  center  is 
on  that  line.  Hence 
we  see  a  circular  arc 
of  light  which  is 
violet  on  the  inner 
edge  and  red  on  the 
outer  edge.  A  sec- 
ond bow  having  the 

n  .  -i  FIG.  446.    Primary  and  secondary  rainbows 

red    on    the    inside 

and  the  violet  on  the  outside  is  often  seen  outside  of  the  one 
just  described,  and  concentric  with  it.  This  bow  arises  from 
rays  which  have  suffered  two  internal  reflections  and  two 
refractions,  in  the  manner  shown  in  Fig.  446. 

477 .  Continuous  Spectra.  Let  a  Bunsen  burner  arranged  to  produce 
a  white  flame  be  placed  behind  a  slit  ,s  (Fig.  447).  Let  the  slit  be  viewed 
through  a  prism  P.  The  spectrum  will  be  a  continuous  band  of  color. 
If  now  the  air  is  admitted 

f. 


at  the  base  of  the  burner, 
and  if  a  clean  platinum  wire 
is  held  in  the  flame  directly 
in  front  of  the  slit,  the  white- 
hot  platinum  will  also  give  a 
continuous  spectrum.* 

All  incandescent  solids 
and  liquids  are  found  to 
give  spectra  of  this  type 
which  contain  all  the 
wave  lengths  from  the  extreme  red  to  the  extreme  violet. 

O 

The  continuous  spectrum  of   a  luminous  gas  flame  is  due  to 

*By  far  the  most  satisfactory  way  of  performing  these  experiments  with 
spectra  is  to  provide  the  class  with  cheap  plate-glass  prisms,  like  those  used 
in  Experiment  50  of  the  authors'  Manual,  rather  than  to  attempt  to  project 
line  spectra. 


FIG.  447.  Arrangement  for  viewing  spectra 


SPECTRA  413 

the  incandescence  of  solid  particles  of  carbon  suspended  in  the 
flame.  The  presence  of  these  solid  particles  is  proved  by  the 
fact  that  soot  is  deposited  on  bodies  held  in  a  white  flame. 

478.  Bright-line  Spectra.     Let  a  bit  of  asbestos  or  a  platinum  wire 
be  dipped  into  a  solution  of  common  salt  (sodium  chloride)  and  held  in 
the  flame,  care  being  taken  that  the  wire  itself  is  held  so  low  that  the 
spectrum  due  to  it  cannot  be  seen.    The  continuous  spectrum  of  the 
preceding  paragraph  will  be  replaced  by  a  clearly  defined  yellow  image 
of  the  slit  which  occupies  the  position  of  the  yellow  portion  of  the 
spectrum.    This  shows  that  the  light  from  the  sodium  flame  is  not  a 
compound  of  a  number  of  wave  lengths,  but  is  rather  of  just  the  wave 
length  which  corresponds  to  this  particular  shade  of  yellow.    The  light 
is  now  coming  from  the  incandescent  sodium  vapor  and  not  from  an 
incandescent  solid,  as  in  the  preceding  experiments. 

Let  another  platinum  wire  be  dipped  in  a  solution  of  lithium  chloride 
and  held  in  the  flame.  Two  distinct  images  of  the  slit,  &•'  and  s"  (Fig.  447), 
will  be  seen,  one  in  red  and  one  in  yellow.  Let  calcium  chloride  be  intro- 
duced into  the  flame.  One  distinct  image  of  the  slit  will  be  seen  in  the 
green  and  another  in  the  red.  Strontium  chloride  will  give  a  blue  and  a 
red  image,  etc.  (The  yellow  sodium  image  will  probably  be  present  in 
each  case,  because  sodium  is  present  as  an  impurity  in  nearly  all  salts.) 

These  narrow  images  of  the  slit  in  the  different  colors  are 
called  the  characteristic  spectral  lines  of  the  substances.  The 
experiments  show  that  incandescent  vapors  and  gases  give  rise 
to  bright-line  spectra,  and  not  continuous  spectra  like  those  pro- 
duced by  incandescent  solids  and  liquids  (see  on  opposite  page). 
The  method  of  analyzing  compound  substances  through  a  study 
of  the  lines  in  the  spectra  of  their  vapors  is  called  spectrum 
analysis.  It  was  first  used  by  Bunsen  in  1859. 

479.  The  solar  spectrum.     Let    a    beam    of    sunlight   pass    first 
through  a  narrow  slit  S  (Fig.  448),  not  more  than  i  millimeter  in  width, 
then  through  a  prism  P,  and  finally  let  it  fall  on  a  screen  S',  as  shown  in 
Fig.  448.    Let  the  position  of  the  prism  be  changed  until  a  beam  of 
white  light  is  reflected  from  one  of  its  faces  to  that  portion  of  the  screen 
which  was  previously  occupied  by  the  central  portion  of  the  spectrum, 


414  COLOR  PHENOMENA 

Then  let  a  fens  L  be  placed  between  the  prism  and  the  slit,  and  moved 
back  and  forth  until  a  perfectly  sharp  white  image  of  the  slit  is  formed 
on  the  screen.  This  adjustment  is  made  in  order  to  get  the  slit  S  and 
the  screen  S'  in  the  positions  of  conjugate  foci  of  the  lens.  Now  let  the 
prism  be  turned  to  its  original 
position.  The  spectrum  on  the 
screen  will  then  consist  of  a 
series  of  colored  images  of  the 
slit  arranged  side  by  side.  This 
is  called  a  pure  spectrum,  to  dis- 
tinguish it  from  the  spectrum 
shown  in  Fig.  440,  in  which  no 
lens  was  used  to  bring  the  rays 
of  each  particular  color  to  a  FlG  448>  Arrangement  for  obtaining  a 
particular  point,  and  in  which  pure  spectrum 

there  was  therefore  much  over- 
lapping of  the  different  colors.    If  the  slit  and  screen  are  exactly  at  con- 
jugate foci  of  the  lens,  and  if  the  slit  is  sufficiently  narrow,  the  spectrum 
will  be  seen  to  be  crossed  vertically  by  certain  dark  lines. 

These  lines  were  first  observed  by  the  Englishman  Wol- 
laston  in  1802,  and  were  first  studied  carefully  by  the  German 
Fraunhofer  in  1814,  who  counted  and  mapped  out  as  many 
as  seven  hundred  of  them.  They  are  called,  after  him,  the 
Fraunhofer  lines.  Their  existence  in  the  solar  spectrum  shows 
that  certain  wave  lengths  are  absent  from  sunlight,  or,  if  not 
entirely  absent,  are  at  least  much  weaker  than  their  neighbors. 
When  the  experiment  is  performed  as  described  above,  it 
will  usually  not  be  possible  to  count  more  than  five  or  six 
distinct  lines. 

480.  Explanation  of  the  Fraunhofer  lines.  Let  the  solar  spec- 
trum be  projected  as  in  §  479.  Let  a  few  small  bits  of  metallic  sodium  be 
laid  upon  a  loose  wad  of  asbestos  which  has  been  saturated  with  alcohol. 
Let  the  asbestos  so  prepared  be  held  to  the  left  of  the  slit,  or  between 
the  slit  and  the  lens,  and  there  ignited.  A  black  band  will  at  once  ap- 
pear in  the  yellow  portion  of  the  spectrum,  in  the  place  where  the  color 
is  exactly  that  of  the  sodium  flame  itself  ;  or,  if  the  focus  was  sufficiently 
sharp  so  that  a  dark  line  could  be  seen  in  the  yellow  before  the  sodium 


SPECTRA 


416 


was  introduced,  this  line  will  grow  very  much  blacker  when  the  sodium 
is  burned.    Evidently,  then,  this  dark  line  in  the  yellow 
part  of  the  solar  spectrum  is  in  some  way  due  to  sodium 
vapor  through  which  the  sunlight  has  somewhere  passed. 

The  experiment  at  once  suggests  the  ex- 
planation of  the  Fraurihofer  lines.  The  white 
light  which  is  emitted  by  the  hot  nucleus  of 
the  sun,  and  which  contained  all  wave  lengths, 
has  had  certain  wave  lengths  weakened  by 
absorption  as  it  passed  through  the  vapors  and 
gases  surrounding  the  sun  and  the  earth.  For 
it  is  found  that  every  gas  or  vapor  ivill  absorb 
exactly  those  wave  lengths  which  it  is  itself  ca- 
pable  of  emitting  when  incandescent.  This  is  for 
precisely  the  same  reason  that  a  tuning  fork 
will  respond  to,  that  is,  abso»b,  only  vibrations 
which  have  the  same  period  as  those  which 
it  is  itself  able  to  emit.  Since,  then,  the  dark 
line  in  the  yellow  portion  of  the  sun's  spectrum 
is  in  exactly  the  same  place  as  the  bright  yellow 
line  produced  by  incandescent  sodium  vapor, 
or  the  dark  line  which  is  produced  whenever 
white  light  shines  through  sodium  vapor,  we 
infer  that  sodium  vapor  must  be  contained  in 
the  sun's  atmosphere.  By  comparing  in  this 
way  the  positions  of  the  lines  in  the  spectra  of 
different  elements  with  the  positions  of  various 
dark  lines  in  the  sun's  spectrum,  many  of  the 
elements  which  exist  on  the  earth  have  been 
proved  to  exist  also  in  the  sun.  For  example, 
Kirchhoff  showed  that  the  four  hundred  sixty 
bright  lines  of  iron  which  were  known  to  him 
were  all  exactly  matched  by  dark  lines  in  the 
solar  spectrum.  Fig.  449  shows  a  copy  of  a  and  iron  spectra 


416  COLOR  PHENOMENA 

photograph  of  a  portion  of  the  solar  spectrum  in  the  middle,, 
and  the  corresponding  bright-line  spectrum  of  iron  each  side 
of  it.  It  will  be  seen  that  the  coincidence  of  bright  and  dark 
lines  is  perfect. 

481.  Doppler's  principle  applied  to  light  waves.  We  have  seen 
(see  The  Doppler  effect,  §  387,  p.  326)  that  the  effect  .of  the  motion  of 
a  sounding  body  toward  an  observer  is  to  shorten  slightly  the  wave  length 
of  the  note  emitted,  and  the  effect  of  motion  away  from  an  observer  is  to 
increase  the  wave  length.  Similarly,  when  a  star  is  moving  toward  the 
earth,  each  particular  wave  length  emitted  will  be  slightly  less  than 
the  wave  length  of  the  corresponding  light  from  a  source  on  the  earth's 
surface.  Hence  in  this  star's  spectrum  all  the  lines  will  be  displaced 
slightly  toward  the  violet  end  of  the  spectrum.  If  a  star  is  moving 
away  from  the  earth,  all  its  lines  will  be  displaced  toward  the  red  end. 
From  the  direction  and  amount  of  displacement,  therefore,  we  can  cal- 
culate the  velocity  with  which  a  star  is  moving  toward  or  receding  from 
the  solar  system.  Observations  of  this  sort  have  shown  that  some  stars 
are  moving  through  space  toward  the  solar  system  with  a  velocity  of 
150  miles  per  second,  while  others  are  moving  away  with  almost  equal 
velocities.  The  whole  solar  system  appears  to  be  sweeping  through 
space  with  a  velocity  of  about  12  miles  per  second ;  but  even  at  this  rate 
it  would  be  at  least  70,000  years  before  the  earth  would  come  into 
the  neighborhood  of  the  nearest  star,  even  if  it  were  moving  directly 
toward  it. 

QUESTIONS  AND  PROBLEMS 

.1.  From  the  table  on  page  403  calculate  how  many  waves  of  red  and 
of  violet  light  there  are  to  an  inch. 

2.  In  what  part  of  the  sky  will  a  rainbow  appear  if  it  is  formed  in 
the  early  morning  ? 

3.  Why  do  we  believe  that  there  is  sodium  in  the  sun? 

4.  What  sort  of  spectrum  should  moonlight  give?   (The  moon  has 
no  atmosphere.) 

5.  If  you  were  given  a  mixture  of  a  number  of  salts,  how  would  you 
proceed,  with  a  Bunsen  burner,  a  prism,  and  a  slit,  to  determine  whether 
or  not  there  was  any  calcium  in  the  mixture  ? 

6.  Draw  a  diagram  of  a  slit,  a  prism,  and  a  lens,  so  placed  as  to- 
form  a  pure  spectrum. 

7.  How  can  you  show  that  the  wave  lengths  of  red  and  green  lights 
are  different,  and  how  can  you  determine  which  one  is  the  longer  ? 


CHAPTER  XXI 


INVISIBLE  RADIATIONS 
RADIATION  FKOM  A  HOT  BODY 

482.  Invisible  portions  of  the  spectrum.  When  a  spectrum 
is  photographed,  the  effect  on  the  photographic  plate  is  found 
to  extend  far  beyond  the  limits  of  the  shortest  visible  violet 
rays.  These  so-called  ultra-violet  rays  have  been  photographed 
and  measured  at  the  Ryerson  Physical  Laboratory,  University 
of  Chicago,  down  to  a  wave  length  of  .00000273 
centimeter,  which  is  only  one  fifteenth  the  wave 
length  of  the  shortest  violet  waves. 

The  longest  rays  visible  in  the  extreme  red 
have  a  wave  length  of  about  .00008  centimeter, 
but  delicate  thermoscopes  reveal  a  so-called 
infra-red  portion  of  the  spectrum,  the  investiga- 
tion of  which  was  carried,  .in  1912,  by  Rubens 
and  von  Baeyer  of  Berlin,  to  wave  lengths  as 
long  as  .03  centimeter,  400  times  as  long  as  the 
longest  visible  rays. 

The  presence  of  these  long  heat  rays  may  be  detected 
by  means  of  the  radiometer  (Fig.  450),  an  instrument 
perfected  by  E.  F.  Nichols  at  Dartmouth.  In  its  common  form  it  consists 
of  a  partially  exhausted  bulb,  within  which  is  a  little  aluminium  wheel 
carrying  four  vanes  blackened  on  one  face  and  polished  on  the  other. 
When  the  instrument  is  held  in  sunlight  or  before  a  lamp,  the  vanes 
rotate  in  such  a  way  that  the  blackened  faces  always  move  away  from 
the  source  of  radiation,  because  they  absorb  ether  waves  better  than  do 
the  polished  faces,  and  thus  become  hotter.  The  heated  air  in  contact 
with  these  faces  then  exerts  a  greater  pressure  against  them  than  does 
the  air  in  contact  with  the  polished  faces. 

417 


FIG.  450.  The 
Crookes  radi- 
ometer 


418 


INVISIBLE  RADIATIONS 


FIG.  451.  A  simple 
thermoscope 


A  still  simpler  way  of  studying  these  long  heat  waves  was  devised 
in  1912  by  TrowJbridge  of  Princeton.    A  rubber  band  AC  (Fig.  451)  a 
millimeter  wide  is  stretched  to  double  its  length  over  a  glass  plate  FGHI, 
and  the  thinnest  possible  glass  staff  ED,  carrying  a 
light  mirror  E  about  2  millimeters  square,  is  placed 
under  the  rubber  band  at  its  middle  point  B.   When 
the  spectrum  is  thrown  upon  the  portion  A  B  of  the 
band,  the  change  in  its  length  produced  by  the 
heating  causes  ED  to   roll,  and  a   spot  of  light 
reflected  from  E  to  the  wall  to  shift  its  position 
by  an  amount  proportional  to  the  heating. 

Let  either  the  radiometer  or  the  thermoscope 
described  above  be  placed  just  beyond  the  red  end  of 
the  spectrum.  It  will  indicate  the  presence  here  of 
heat  rays  of  even  greater  energy  than  those  in  the 
visible  spectrum.  Again,  let  a  red-hot  iron  ball  and  one  of  the  detectors 
be  placed  at  conjugate  foci  of  a  large  mirror  (Fig.  452).  The  invisible 
heat  rays  will  be  found  to  be  reflected  and  focused  just  as  are  light 
rays.  Next  let  a  .flat  bottle  filled  with  water  be  inserted  between  the 
detector  and  any  source  of  heat.  It  will  be  found  that  water,  although 
transparent  to  light  rays,  absorbs  nearly  all  of  the  infra-red  rays.  But 
if  the  water  is  replaced  by  carbon  bisulphide,  the  infra-red  rays  will 
be  freely  transmitted, 
even  though  the  liquid 
is  rendered  opaque  to 
light  waves  by  dissolv- 
ing iodine  in  it. 

483.  Radiation  and 
temperature.  All  bod- 
dies,  even  such  as  are 
at  ordinary  tempera- 
tures, are  continually 
radiating  energy  in  the  form  of  ether  waves.  This  is  proved 
by  the  fact  that  even  if  a  body  is  placed  in  the  best  vacuum 
obtainable,  it  continually  falls  in  temperature  when  surrounded 
by  a  colder  body,  —  for  example,  liquid  air.  The  ether  waves 
emitted  at  ordinary  temperatures  are  doubtless  very  long  as 
compared  with  light  waves.  As  the  temperature  is  raised, 


FIG.  452.    Reflection  of  infra-red  rays 


RADIATION  FROM  A  HOT  BODY  419 

more  and  more  of  these  long  waves  are  emitted,  but  shorter 
and  shorter  waves  are  continually  added.  At  about  525°  C. 
the  first  visible  waves,  that  is,  those  of  a  dull  red  color, 
begin  to  appear.  From  this  temperature  on,  owing  to  the 
addition  of  shorter  and  shorter  waves,  the  color  changes 
continuously,  —  first  to  orange,  then  to  yellow,  and,  finally, 
between  800°  C.  and  1200°  C.,  to  white.  In  other  words,  all 
bodies  get  "red-hot"  at  about  525°  C.  and  "white-hot"  at 
from  800°  C.  to  1200°  C. 

Some  idea  of  how  rapidly  the  total  radiation  of  ether  waves 
increases  with  increase  of  temperature  may  be  obtained  from 
the  fact  that  a  hot  platinum  wire  gives  out  thirty-six  times 
as  much  light  at  1400°  C.  as  it  does  at  1000°  C.,  although 
at  the  latter  temperature  it  is  already  white-hot  The  radi- 
ations from  a  hot  body  are  sometimes  classified  as  heat 
rays,  light  rays,  and  chemical,  or  actinic,  rays.  The  classifi- 
cation is,  however,  misleading,  since  all  ether  waves  are  heat 
waves  in  the  sense  that,  when  absorbed  by  matter,  they  pro- 
duce heating  effects,  that  is,  molecular  motions.  Radiant 
heat  is,  then,  the  radiated  energy  of  ether  waves  of  any  and  all 
wave  lengths. 

484.  Radiation  and  absorption.  Although  all  substances 
begin  to  emit  waves  of  a  given  wave  length  at  approximately 
the  same  temperature,  the  total  rate  of  emission  of  energy  at 
a  given  temperature  varies  greatly  with  the  nature  of  the 
radiating  surface.  In  general,  experiment  shows  that  surfaces 
which  are  good  absorbers  of  ether  radiations  are  also  good  radiators. 
From  this  it  follows  that  surfaces  which  are  good  reflectors,  like 
the  polished  metals,  must  be  poor  radiators. 

Thus,  let  two  sheets  of  tin,  5  or  10  centimeters  square,  one  brightly 
polished  and  the  other  covered  on  one  side  with  lampblack,  be  placed 
in  vertical  planes  about  10  centimeters  apart,  the  lampblacked  side  of 
one  facing  the  polished  side  of  the  other.  Let  a  small  ball  be  stuck 
with  a  bit  of  wax  to  the  outer  face  of  each.  Then  let  a  hot  metal 


420  INVISIBLE  KADIATIONS 

plate  or  ball  (Fig.  453)  be  held  midway  between  the  two.  The  wax  on 
the  tin  with  the  blackened  face  will  melt  and  its  ball  will  fall  first, 
showing  that  the  lampblack  ab- 
sorbs the  heat  rays  faster  than 
does  the  polished  tin.  Now 
let  two  blackened  glass  bulbs 
be  connected,  as  in  Fig.  454, 
through  a  U-tube  containing 
colored  water,  and  let  a  well- 
polished  tin  can,  one  side  of 

which  has  been  blackened,  be      FlG>453<  Goodre_      FlG.  454.  Goodab- 
filled  with   boiling  water  and     flectorg    ^    pQor      ^^    ^    ^ 
placed  between  them.   The  mo-  absorbers  radiators 

tion  of  the  water  in  the  U-tube 

will  show  that  the  blackened  side  of  the  can  is  radiating  heat  much  more 
rapidly  than  the  other,  although  the  two  are  at  the  same  temperature. 


QUESTIONS  AND  PROBLEMS 

1.  The  atmosphere  is  transparent  to  most  of  the  sun's  rays.    Why 
are  the  upper  regions  of  the  atmosphere  so  much  colder  than  the  lower 
regions  ? 

2.  When  one  is  sitting  in  front  of  an  open-grate  fire,  does  he  receive 
most  heat  by  conduction,  by  convection,  or  by  radiation  ? 

3.  Sunlight  in  coming  to  the  eye  travels  a  much  longer  air  path 
at  sunrise  and  sunset  than  it  does  at  noon.    Since  the  sun  appears 
red  or  yellow  at  these  times,  what  rays  are  absorbed  most  by  the 
atmosphere  ? 

4.  Glass  transmits  all  the  visible  waves,  but  does  not  transmit  the 
long  infra-red  rays.   From  this  fact  explain  the  principle  of  the  hotbed. 

5.  Which  will  be  cooler  on  a  hot  day,  a  white  hat  or  a  black  one? 

6.  Will  tea  cool  more  quickly  in  a  polished  or  in  a  tarnished  metal 
vessel ? 

7.  Which  emits  the  more  red  rays,  a  white-hot  iron  or  the  same  iron 
when  it  is  red-hot  ? 

8.  Liquid-air  flasks    and   thermos    bottles   are   double-walled   glass 
vessels  with  a  vacuum  between  the  walls.    Liquid  air  will  keep  many 
times  longer  if  the  glass  walls  are  silvered  than  if  they  are  not.    Why  ? 
Why  is  the  space  between  the  walls  evacuated  ? 


ELECTRICAL  RADIATIONS 


421 


ELECTRICAL  RADIATIONS 

485.  Proof  that  the  discharge  of  a  Leyden  jar  is  oscillatory. 

We  found  in  §  408,  p.  346,  that  the  sound  waves  sent  out 
by  a  sounding  tuning  fork  will  set  into  vibration  an  adjacent 
fork,  provided  the  latter  has  the  same  natural  period  as  the 
former.  Following  is  the  complete  electrical  analogy  of  this 
experiment. 

Let  the  inner  and  outer  coats  of  a  Leyden  jar  A  (see  Fig.  455)  be 
connected  by  a  loop  of  wire  cdef,  the  sliding  crosspiece  de  being  arranged 
so  that  the  length  of  the  loop  may  be  altered  at  will.  Also  let  a  strip 
of  tin  foil  be  brought  over  the  edge  of  this  jar  from  the  inner  coat  to 
within  about  1  millimeter 
of  the  outer  coat  at  C.  Let 
the  two  coats  of  an  exactly 
similar  jar  B  be  connected 
with  the  knobs  n  and  n  by 
a  second  similar  wire  loop 
of  fixed  length.  Let  the 
two  jars  be  placed  side  by 
side  with  their  loops  par-  FlG  455  Sympathetic  electrical  vibrations 
allel,  and  let  the  jar  B  be 

successively  charged  and  discharged  by  connecting  its  coats  with  a 
static  machine  or  an  induction  coil.  At  each  discharge  of  jar  B  through 
the  knobs  n  and  n  a  spark  will  appear  in  the  other  jar  at  C,  provided 
the  crosspiece  de  is  so  placed  that  the  areas  of  the  two  loops  are  equal. 
When  de  is  slid  along  so  as  to  make  one  loop  considerably  larger  or 
smaller  than  the  other,  the  spark  at  C  will  disappear. 

The  experiment  therefore  demonstrates  that  two  electrical 
circuits,  like  two  tuning  forks,  can  be  tuned  so  as  to  respond  to 
each  other  sympathetically,  and  that  just  as  the  tuning  forks 
will  cease  to  respond  as  soon  as  the  period  of  one  is  slightly 
altered,  so  this  electric  resonance  disappears  when  the  exact 
symmetry  of  the  two  circuits  is  destroyed.  Since,  obviously, 
this  phenomenon  of  resonance  can  occur  only  between  systems 
which  have  natural  periods  of  vibration,  the  experiment  proves 
that  the  discharge  of  a  Leyden  jar  is  a  vibratory,  that  is,  an 


422  INVISIBLE  RADIATIONS 

oscillatory,  phenomenon.  As  a  matter  of  fact,  when  such  a 
spark  is  viewed  in  a  rapidly  revolving  mirror,  it  is  actually  found 
to  consist  of  from  ten  to  thirty  flashes  following  each  other  at 
equal  intervals.  Fig.  456  is  a  photograph  of  such  a  spark. 

In  spite  of  these  oscillations  the  whole  discharge  may  be 
made  to  take  place  in  the  incredibly  short  time  of  I,OOQ,OOO 
of  a  second.  This  fact,  coupled 
with  the  extreme  brightness  of 
the  spark,  has  made  possible  the 
surprising  results  of  so-called 

instantaneous  electric-spark  pho- 

-,  r~,          ,    ,  .,  FIG.  456.    Oscillations  of  the 

tography.      The   plate   opposite  electric  spark 

page  425  shows  the  passage  of 

a  bullet  through  a  soap  bubble.  The  film  was  rotated  continu- 
ously instead  of  intermittently,  as  in  ordinary  moving-picture 
photography.  The  illuminating  flashes,  5000  per  second,  were 
so  nearly  instantaneous  that  the  outlines  are  not  blurred. 

486.  Electric  waves.  The  experiment  of  §  485  demonstrates 
not  only  that  the  discharge  of  a  Leyden  jar  is  oscillatory  but 
also  that  these  electrical  oscillations  set  up  in  the  surrounding 
medium  disturbances,  or  waves  of  some  sort,  which  travel  to  a  t 
neighboring  circuit  and  act  upon  it  precisely  as  the  air  waves 
acted  on  the  second  tuning  fork  in  the  sound  experiment. 
Whether  these  are  waves  in  the  air,  like  sound  waves,  or  dis- 
turbances in  the  ether,  like  light  waves,  can  be  determined  by 
measuring  their  velocity  of  propagation.  The  first  determina- 
tion of  this  velocity  was  made  by  Heinrich  Hertz  (see  oppo- 
site p.  102)  in  1888.  He  found  it  to  be  precisely  the  same  as 
that  of  light,  that  is,  300,000  kilometers  per  second.  This 
result  shows,  therefore,  that  electrical  oscillations  set  up  ivaves  in 
the  ether.  These  waves  are  now  known  as  Hertzian  waves. 

The  length  of  the  waves  emitted  by  the  oscillatory  spark 
of  instantaneous  photography  is  evidently  very  great,  namely, 
about  VoVoV.AV  =  30  meters>  since  the  velocity  of  light  is 


ELECTRICAL  RADIATIONS  423 

300,000,000  meters  per  second,  and  since  there  are  10,000,000 
oscillations  per  second ;  for  we  have  seen  in  §  382,  p.  323, 
that  wave  length  is  equal  to  velocity  divided  by  the  number 
of  oscillations  per  second.  By  diminishing  the  size  of  the  jar 
and  the  length  of  the  circuit  the  length  of  the  waves  may  be 
greatly  reduced.  By  causing  the  electrical  discharges  to  take 
place  between  two  balls  only  a  fraction  of  a  millimeter  in 
diameter,  instead  of  between  the  coats  of  a  condenser,  elec- 
trical waves  have  been  obtained  as  short  as  .3  centimeter,  — 
only  ten  times  as  long  as  the  longest  measured  heat  waves. 

487.  Detection  of  electric  waves.  In  the  experiment  of  §  485 
we  detected  the  presence  of  the  electric  waves  by  means  of  a 
small  spark  gap  C  in  a  circuit  almost  identical  with  that  in 
which  the  oscillations  were  set  up.    The  visible  spark  may  be 
employed  for  the  detection  of  waves  many  feet  away  from 
the  source,  but  for  detecting  the  feeble  waves  which  come  in 
from  a  source  hundreds  or  thousands  of  miles  away  we  must 
depend  upon  sounds  produced  in  an  extremely  sensitive  tele- 
phone receiver,  as  explained  in  the  next  section. 

488.  Wireless  telegraphy.   Commercial  wireless  telegraphy 
was  realized  in  1896  by  Marconi  (see  opposite  p.  316),  eight 
years  after  the   discovery  of  Hertzian  waves.    The  essential 
elements  of  a  tuned  wave-train,  or  "  spark,"  system  of  wireless 
telegraphy  are  as  follows: 

The  key  K  at  the  transmitting  station  (Fig.  457,  (1)  )  is  depressed 
to  allow  a  current  from  the  alternator  A  to  pass  through  the  primary 
coil  P  of  a  transformer  T"13  the  frequency  of  the  alternations  in  practice 
being  usually  about  500  cycles  per  second.  The  high-voltage  current- 
induced  in  the  secondary  S  charges  the  condenser  Cl  until  its  potential 
rises  high  enough  to  cause  a  spark  discharge  to  take  place  across  the 
gap  s.  This  discharge  of  C^  is  oscillatory  (§  485),  and  the  oscillations 
thus  produced  in  the  condenser  circuit  containing  Cv  s,  and  L1  may,  in 
a  low-power  sfiort-wave  transmitting  set,  have  a  frequency  as  high  as 
1,000,000  per  second.  An  oscillation  frequency  much  lower  than  this 
is  generally  used  and  is  subject  to  the  control  of  the  operator  through 


424 


INVISIBLE  RADIATIONS 


the  sliding  contact  c,  precisely  as  in  the  case  illustrated  in  Fig.  455. 
The  oscillations  in  the  condenser  circuit  induce  oscillations  in  the  aerial- 
wire  system,  which  is  tuned  to  resonance  with  it  through  the  sliding 
contact  6-'. 


(1) 


(2) 


FIG.  457.    Transmitting  and  receiving  stations  for  wireless  telegraphy 


As  long  as  the  key  K  is  kept  closed  (assuming  a  500-cycle  alternator 
to  be  used),  1000  sparks  per  second  occur  at  s,  and  therefore  a  regular 
series  of  1000  wave  trains  (Fig.  458)  pass  off  from  the  aerial  every 
second  and  move  away  with  the  velocity  of  light.  If  the  oscillations 
which  produce  a  wave  train  have  a  frequency 
of,  say,  500,000  per  second,  each  wave  in  the 

It     ,  300,000,000 
wave  train  has  a  length  of 


Direction  of 
Propagation 


500,000 

600  meters  ;  and  if  these  wave  trains  are 
produced  at  the  rate  of  1000  per  second, 
they  follow  each  other,  at  regular  distances 
of  300,000  meters,  that  is,  nearly  200  miles. 
The  waves  sent  out  by  the  aerial  system 
of  the  transmitting  station  induce  like  os- 
dilations  in  the  distant  aerial  system  of  the 
receiving  station  (Fig.  457,  (2)  ),  which  is 

tuned  to  resonance  with  it.  In  case  the  receiving  aerial  must  be  tuned 
to  respond  to  very  long  waves,  the  switch  0  is  closed  to  cut  out  the 
condenser  C2,  and  the  inductance,  or  loading  coil,  B^  is  used  ;  whereas, 
to  tune  to  very  short  waves,  the  switch  0  is  opened  and  the  variable 


FIG.  458.   One  wave  train 
from  oscillatory  discharge 


itih   WIKELESS  TELEPHONE  UTILIZED  IN  AVIATION 

One  of  the  most  notable  developments  of  the  war  was  the  directing  of  a  squadron 
of  airplanes  in  intricate  maneuvers  by  wireless  telephone  either  from  the  ground 
or  by  the  commander  in  the  leading  plane.  The  upper  panel  shows  the  pilot  and 
the  observer  conversing  with  special  apparatus  designed  to  eliminate  plane  noises, 
and  the  lower  panel  shows  President  Wilson  talking  by  wireless  to  airplanes 


CINEMATOGRAPH  FILM  OF  A  BULLET  FIRED  THROUGH  A  SOAP  BUBBLE 

The  flight  of  the  missile  may  be  followed  easily.   It  will  be  seen  that  the  bubble 

breaks,  not  when  the  bullet  enters,  but  when  it  emerges.  (From  "  Moving  Pictures," 

by  F.  A.  Talbot.  Courtesy  of  J.  B.  Lippincott  Company) 


ELECTRICAL  RADIATIONS  425 

condenser  C'0  is  brought  into  use,  the  loading  coil  not  being  utilized.1 
The  oscillations  in  the  aerial  circuit  of  the  receiving  station  induce 
exactly  similar  ones  in  the  detector  circuit,  which  is  tuned  to  resonance 
with  the  receiving  aerial  by  means  of  L2,  B2,  and  C3.  The  so-called 
detector  of  these  oscillations  may  be  simply  a  crystal  of  galena  D  in 
series  with  the  telephone  receivers  R.  This  crystal,  like  the  tungar 
rectifier  of  §  374,  has  the  property  of  transmitting  a  current  in  one 
direction  only.2  Were  it  not  for  this  property  the  telephone  could  not 
be  used  as  a  detector,  because  its  diaphragm  cannot  vibrate  with  a  fre- 
quency of  the  order  of  a  million;  and  even  if  it  could,  it  would  produce 
sound  waves  far  above  the  limit  of 
hearing.  Because  of  this  rectifying 
property  of  the  crystal  the  receiver 
diaphragm  is  drawn  in  only  once 
while  the  oscillations  produced  by  a 
given  wave  train  last,  this  effect  being- 
due  to  the  rectified  pulsating  current 
which  passes  in  one  direction  through 
the  receivers  and  then  ceases  until  the 
oscillations  due  to  the  next  spark  ar-  FlG  459  United  gtates  navy 
rive.  Since  1000  of  the  intermittent  standard  radio  receivers 

wave  trains  strike  upon  the  aerial  each 

second,  the  operator  at  the  receiving  station  hears  a  continuous  musical 
note  of  this  pitch  as  long  as  the  key  K  is  depressed.  The  working  of  the  key, 
however,  as  in  ordinary  telegraphy,  breaks  the  regular  series  of  wave 
trains  into  groups  of  wave  trains,  so  that  the  short  and  long  notes  heard  in 
the  receivers  (Fig.  459)  correspond  to  the  dots  and  dashes  of  telegraphy. 
The  receiving  circuit,  when  tuned  as  shown  in  Fig.  457,  (2),  is  highly 
selective ;  that  is,  it  will  not  pick  up  waves  of  other  periods.  The  loading 
coils  Bl  and  52,  as  well  as  the  two  variable  condensers  C2  and  C3,  are 
usually  omitted  from  small  amateur  receiving  sets ;  but  when  this  is 
done,  the  receiving  set  is  less  selective  and  less  sensitive.  The  resist- 
ance of  the  receivers  is  so  high,  usually  from  1000  to  4*000  ohms,  that 

1  In  the  diagram  an  arrow  drawn  diagonally  across  a  condenser  indicates 
that,  for  the  sake  of  tuning,  the  condenser  is  made  adjustable.  Similarly,  an 
arrow  across  two  circuits  coupled  inductively,  like  the  primary  and  secondary 
of  the  "oscillation  transformer  "  J"0,  indicates  that  the  amount  of  interaction 
of  the  two  circuits  can  be  varied,  as,  for  example,  by  sliding  one  coil  a  longer 
or  shorter  distance  inside  the  other. 

2  Crystal  detectors  have  been  largely  superseded  by  the  "audion  "  for  both 
wireless  telegraphy  and  wireless  telephony. 


426  INVISIBLE  RADIATIONS 

they  do  not  interfere  with  the  oscillations  of  the  condenser  system 
across  which  they  are  placed.  The  receiving  station  shown  in  Pig.  457,  (2), 
may  also  be  used  for  receiving  tvireless- telephone  messages.  The  simplified 
circuit  of  an  audion  receiving  station  is  shown  opposite  page  441. 

Although  the  spark,  or  wave-train,  system  of  wireless  teleg- 
raphy is  still  widely  used,  the  "  continuous  wave  "  system  is 
rapidly  displacing  it.  Just  as  sound  waves  differing  slightly 
in  frequency  combine  to  produce  the  phenomenon  of  beats 
(§  890),  so  electrical  oscillations  differing  in  frequency  give, 
when  combined,  a  "beat  effect."  For  instance,  if  electrical 
oscillations  of,  say,  30,000  per  second  and  31,000  per  second 
combine,  beats  will  occur  at  the  rate  of  1000  per  second, 
which  is  a  frequency  within  the  limit  of  hearing.  The  elec- 
trical oscillations  mentioned  above  have  a  frequency  beyond 
the  limit  of  hearing  and  hence  are  said  to  have  radio  fre- 
quency ;  but  the  beats  being  within  the  range  of  hearing 
have  an  audio  frequency.  Now  let  us  assume  that  there  is 
at  the  transmitting  station  an  alternating-current  generator 
which  throws  into  the  aerial  powerful  undamped  oscillations 
of  30,000  per  second;  and  suppose  further  that  at  the  receiv- 
ing station  there  is  an  oscillation  generator  which  maintains 
relatively  weak  oscillations  of  31,000  per  second  in  the  local 
receiving  aerial.  These  weak  oscillations  produced  in  the 
receiving  aerial  by  the  local  generator  make  no  sound  in  the 
receiver,  being  above  the  limit  of  hearing ;  but  whenever,  and 
as  long  as,  the  operator  at  the  transmitting  station  depresses 
his  key,  waves  come  in  at  the  rate  of  30,000  per  second, 
strike  against  the  receiving  aerial  and  develop  therein  weak 
oscillations  which  combine  with  those  already  present  to  make 
1000  beats  per  second.  These  beat  effects  are  rectified  by  a 
crystal  or  by  a  vacuum  tube  and  passed  through  the  receiver. 
The  listener,  therefore,  hears  long  and  short  musical  sounds 
just  as  he  does  when  receiving  by  the  spark  system.  The 
beat  method  of  receiving  is  called  the  heterodyne  system. 


ELECTKICAL  RADIATIONS  427 

489.  Modulated  continuous  waves.*  The  vibrations  consti- 
tuting articulate  speech  are  exceedingly  complex,  as  may  be 
seen  from  an  inspection  of  the  full-page  halftone  opposite 
page  346.  Because  of  this  complexity  it  is  impossible  to  trans- 
mit speech  by  means  of  discontinuous  waves  (Fig.  460)  such 
as  are  employed  in  the  system  of  spark  telegraphy  described 
in  the  preceding  section.  The  parts  of  the  voice  lost  because 

Direction  of  propagation >• 

-4 4 4 — -4 4 — -4 — -* — -4- 

FIG.  460.    A  series  of  wave  trains 

of  the  gaps  between  the  wave  trains  would  render  the  language 
unintelligible.  Theoretically  the  voice  could  be  transmitted 
by  continuous  electromagnetic  waves  having  the  frequencies 
of  voice  vibrations,  but  such  a  method  is  entirely  impracti- 
cable on  account  of  the  enormous  length  of  aerial  needed 
to  produce  such  long  waves  and  the  tremendous  amount  of 
power  which  would  be  required.  Therefore,  the  only  satis- 
factory method  thus  far  developed  is  to  transmit  speech 


FIG.  461.    Continuous,  or  carrier,  waves  of  radio  frequency 

on    continuous,    or    "  carrier,"    waves  (Fig.  461)    having    a 
frequency  (radio  frequency)  above  the  limit  of  hearing. 

At  the  sending  station  the  continuous  waves  (Fig.  461) 
are  "  modulated "  by  the  voice  at  the  transmitter ;  that  is, 
the  sound  waves  of  the  voice  act  upon  the  apparatus  in  such 
a  way  as  to  alter  the  otherwise  uniform  amplitude  of  the  series 
of  continuous  waves  (Fig.  462).  These  "modulated"  con- 
tinuous waves  on  reaching  the  aerial  of  the  receiving  station 
produce  corresponding  oscillatory  currents  in  the  wires  of  the 

*  The  pupil  should  master  §§  374,  375,  376,  485,  486,  487,  and  488  before 
reading  the  six  sections  following. 


428 


INVISIBLE  RADIATIONS 


aerial.  By  means  of  a  crystal  or  a  vacuum  tube,  the  oscilla- 
tory currents  are  rectified  into  a  series  of  unidirectional  elec- 
trical currents,  or  pulses,  somewhat  after  the  mann-er  indicated 


FIG.  462.    Modulated  radio-frequency  waves 

in  Fig.  463.  These  variable  pulses  of  radio  frequency,  on 
reaching  the  telephone  receivers  of  the  listener,  produce  dia- 
phragm vibrations  of  low  frequencies  (audio  frequencies),  which 


(Innnnnfl 


Innnflnnr 


FIG.  463.    Rectified  oscillations 


rarely  go  outside  the  limits  of  100  and  3000  vibrations  per 
second.  They  are  represented  by  the  irregular  line  in  Fig.  464. 
The  vibrations  of  the  diaphragms  of  the  receivers,  therefore, 


FIG.  464.    Audio-frequency  variations 

correspond  to  the  vibrations  of  the  voice  of  the  speaker  at 
the  distant  transmitting  station. 

490.  Method  of  producing  continuous  waves.  One  of  the 
most  important  of  the  different  means  of  producing  high- 
power  continuous  waves  is  by  use  of  the  Alexanderson  high- 
frequency  alternator  (see  on  opposite  page).  This  is  an 
alternating-current  dynamo  made  in  various  powers  up  to 
200  kilowatts  (=  268  horse  power),  the  rotor  in  some  of  the 
machines  having  the  very  high  speed  of  20,000  revolutions 
per  minute.  For  transoceanic  telegraphy  these  machines  cause 
currents  of  from  600  to  1200  amperes  to  oscillate  in  the  sending 
aerial.  This  powerful  sustained  oscillation  of  electrons  in  an 
aerial  produces  continuous  electromagnetic  waves  (Fig.  461). 


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ELECTRICAL  RADIATIONS 


429 


491.  The  vacuum  tube.  There  are  several  devices  by  which 
the  voice  waves  may  modulate,  or  vary  the  amplitude  of,  the 
carrier  waves,  the  most  important  being  the  highly  exhausted 
"  vacuum  tube  "  (see  Fig.  465,  the  halftone  opposite  p.  441, 
and  the  drawing  and  legend  opposite  p.  33). 

In  attempting  to  reach  an  understanding  of  an  "  audion  " 
amplifier  or  other  form  of  vacuum  tube,  it  is  well  to  remember 


(in  center) 
Grid  (surrounding  filament) 

late  (surrounding  grid  — 
'  front  half  cut  away) 


Terminals          ^—Filament 

Filament 

• 

FIG.  465.    A  popular  form  of  vacuum  tube  used  in  radio  receiving 

that  a  current  of  electricity  is  a  stream  of  negative  elec- 
trons which,  when  passing  through  a  vacuum,  move  with 
enormous  velocity  (thousands  of  miles  per  second  (§  498)), 
but  when  passing  along  a  wire  (ordinary  conduction)  move 
quite  slowly  (a  few  centimeters  per  second).  Now  we  found 
in  studying  the  tungar  rectifier  (§  374)  that  these  negative 
electrons  escape  freely  from  an  incandescent  filament  under 
certain  conditions.  When  the  battery  B  (Fig.  466)  has  its 
+  terminal  connected  to  the  plate  P  of  the  vacuum  tube  and 


430 


INVISIBLE  RADIATIONS 


FIG.  466.    A  two-electrode 
vacuum  valve 


its  —  terminal  to  the  filament  F,  no  current  can  flow  across 
the  vacuum  so  long  as  the  filament  is  cold.  When,  however,  the 
filament  is  maintained  at  incandescence  by  a  battery  J,  the 
negative  electrons  escape  from  it  and  are  drawn  in  a  steady 
stream  across  the  vacuum  by  the 
attraction  of  the  +  plate  P.  This 
flow  of  —  electrons  from  filament  to 
plate  constitutes  what  is  considered 
by  convention  to  be  a  current  of 
electricity  flowing  the  opposite  way, 
namely,  from  plate  to  filament.  We 
now  see  how  battery  J,  by  keeping 
the  filament  in  a  state  of  incandes- 
cence, merely  establishes  and  main- 
tains one  of  the  conditions  under  which  battery  B  may  discharge 
a  steady  current  through  the  vacuum.  No  electronic  flow 
from  the  cold  plate  to  the  filament  is  ever  possible,  because 
cold  bodies  do  not,  except  in  rare  instances  (see  pp.  441  ff.) 
eject  electrons  from  themselves.  The  vacuum  tube  can 
therefore  be  utilized  as  a 
vacuum  valve,  or  rectifier,  for 
evidently,  if  a  source  of  alter- 
nating current  be  substituted 
for  the  direct  current  source 
(battery  B),  the  vacuum. valve 
would  transmit  current  in  one 
direction  only,  half  of  each 
cycle  being  held  in  check. 

If  a  screen  of  fine  wire  G, 
known  as  a  1{  grid,"  be  introduced  between  the  filament  and 
the  plate  of  Fig.  466  (see  Fig.  467)  and  the  grid  be  main- 
tained at  a  sufficiently  high  —  potential  by  a  battery  (7,  the 
—  electrons  are  repelled  back  into  the  incandescent  filament 
and  cannot  escape  from  it,  and  thus  the  electronic  flow  is 


FIG.  467.    A  three-electrode  vacuum 
tube 


ELECTRICAL  RADIATIONS 


431 


completely  checked;  that  is,  no  current  flows  across  the  vacuum. 
If  now  the  —  potential  of  the  grid  be  varied,  say,  from  zero 
to  the  amount  required  to  stop  the  electronic  flow,  the  current 
from  battery  B  through  the  vacuum  is  thereby  varied  from 
the  possible  maximum  in  Fig.  466  to  zero.  Variation  of  the 
grid  potential,  therefore,  affords  us  a  means  of  controlling 
and  of  varying  the  flow 
of  current  through  a 
vacuum  tube.  Indeed, 
it  is  found  that  slight 
changes  in  the  grid  volt- 
age produce  surpris- 
ingly great  changes  in 
the  current  through  the 
tube  ;  that  is,  the  tube 
is  an  amplifier. 

492.  Transfer  of  energy 
through  a  condenser.  In 
Fig.468,(l),theE.M.F. 


generator 


\Cm 


Condenser 


(1) 


The  lamp  docs  not  burn 


A.  C.  generator 


(2) 


"Too 


Condenser 


The  lamp  burns 


FIG.  468.    Energy  transferred  through  a 
condenser 


of  the  direct-current  dy- 
namo causes  a  rush  of 
electrons  out  of  one  side 
of  the  condenser  while 
electrons  to  an  equal 
extent  rush  into  the  other  side.  The  sides  of  the  condenser 
are  thus  charged  -f-  and  —  and  they  remain  so  as  long  as  the 
dynamo  runs.  It  is  evident  that  under  these  conditions  there 
is  no  flow  of  current  and  that  consequently  the  lamp  does 
not  burn.  If,  however,  an  alternating-current  dynamo  is  used 
(Fig.  468,  (2)),  the  alternating  E.M.F.  causes  an  alternat- 
ing rush  of  electrons  which  charges  the  condenser  first  one 
way  and  then  the  opposite  way.  It  is  clear,  then,  that  with 
an  alternating-current  dynamo,  lamp,  and  condenser  thus 
arranged  we  may  have  an  alternating  current  through  the 


432 


INVISIBLE  RADIATIONS 


lamp  which  will  cause  it  to  light  up.  Condensers  of  variable 
capacity  are  widely  used  in  the  circuits  of  wireless  apparatus 
as  aids  in  tuning,  and  they  permit  passage  of  electrical  energy 
in  the  manner  explained  above. 

493.  The  receiving  station.  Fig.  469  represents  a  "regenera- 
tive "  receiving  circuit  capable  of  receiving  long  or  short 
waves.  When  the  modulated  waves  (Fig.  462)  reach  the 
tuned  aerial  of  the  receiving  station,  they  develop  therein 
feeble  electrical  oscillations  which  induce  oscillations  in  LZ 
of  the  tuned  grid  circuit.  This  varies  the  potential  of  the 


FIG.  469.    A  regenerative  receiving  circuit 

grid  6r2,  thus  causing  corresponding  changes  in  the  strength 
of  the  electronic  current  flowing  from  the  incandescent  fila- 
ment FZ  to  the  plate  P2  and  thence  back  through  the  plate 
coil  PC.  The  plate  circuit  is  so  tuned  with  respect  to  the 
grid  circuit  that  these  current  variations  in  the  plate  coil 
react  inductively  on  the  coil  L2  connected  with  the  grid  cir- 
cuit to  strengthen  the  original  grid-circuit  current.  This 
intensifies  the  variations  in  potential  at  the  grid,  which  in 
turn  intensifies  the  variations  in  strength  of  the  electronic 
current  from  filament  to  plate,  and  this  still  further  intensi- 
fies the  variations  in  potential  at  the  grid,  and  so  on,  up  to 


ELECTRICAL  RADIATIONS 


433 


the  limit  of  the  electron  supply  in  the  tube.  This  is  the 
Armstrong  regenerative  principle  by  which  very  feeble  oscilla- 
tions produced  by  the  incoming  waves  may  be  amplified  and 
then  used  to  intensify  the  original  oscillations.  The  energy 
for  regeneration  comes  from  the  battery  BZ.  When  the  tube  is 
in  use  the  grid  tends  to  accumulate  a  negative  charge  which, 
as  we  have  seen  (§  491),  would  tend  to  block  completely 
the  action  of  the  tube.  Therefore,  a  high-resistance  grid  leak 
r  is  shunted  around  the  condenser  (74  to  permit  the  return 


Variometer 


FIG.  470.    A  two-variometer  tuned-plate-circuit  for  receiving  short  waves 

of  such  a  detrimental  accumulation  of  electrons  to  the  fila- 
ment F^  by  way  of  r  and  L2.  The  telephone  receivers  used 
in  wireless  work  contain  thousands  of  turns  of  very  fine  wire 
wound  upon  iron  and  because  of  the  consequent  "  choke- 
coil  "  effect,  or  impedance,  of  these  coils  for  high-frequency 
changes  in  current  strength,  the  mcfo'o-frequency  variations 
(Fig.  463)  of  the  plate  current  pass  largely  by  way  of  the 
variable  condenser  (79,  while  the  slower  aw^'o-frequency  varia- 
tions (Fig.  464)  of  the  plate  current  pass  readily  through 
the  receivers  to  actuate  the  diaphragm. 

Fig.  470  shows  a  two-variometer  circuit  for  the  reception 
of  short  waves.    A  variometer  is  a  variable  inductance  used 


434  INVISIBLE  BADIATIONS 

for  tuning  and  it  consists  of  two  coils  in  series,  one  of  which 
revolves  within  the  other.  If  current  is  passed  through  the 
variometer  when  the  inner  coil  is  turned  so  that  its  magnetic 
field  combines  with  that  of  the  other  coil  to  make  the  greatest 
resultant  magnetic  field,  the  inductance  of  the  variometer  is 
found  to  have  its  greatest  value  and  the  adjustment  is  then 
for  the  longer  waves,  or  slower  oscillations.  If  the  inner  coil 
is  now  turned  through  180°,  the  resultant  magnetic  field  is 
at  minimum  strength ;  and,  because  of  the  small  inductance, 
the  variometer  is  adjusted  to  the  shorter  waves.  Intermediate 
positions  of  the  inner  coil  are  used  for  wave  lengths  lying 
between  these  limits.  Complete  tuning  is  accomplished  by 
use  of  the  two  variometers,  the  two  variable  condensers  and 
the  sliding  contact  on  the  aerial  coil. 

494.  The  transmitting  station.  The  vacuum  tube  may  be 
used  not  only  as  a  rectifier,  a  detector,  a  modulator,  and  an 
amplifier,  but  under  certain  conditions  as  a  generator  of  oscil- 
lations varying  over  an  extremely  wide  range  of  frequency  — 
from  less  than  1  oscillation  per  second  to  300,000,000  or 
more  per  second.  Nearly  all  present-day  "  broadcasting "  is 
done  by  use  of  vacuum-tube  generators.  For  high-power 
long-distance  transmission  banks  of  vacuum-tube  amplifiers 
may  be  used  to  throw  into  an  aerial  an  aggregate  power  of 
many  hundreds  of  kilowatts.  Indeed,  at  the  present  time 
rapid  progress  is  being  made  in  the  experimental  construc- 
tion of  power  tubes  each  one  of  which  is  capable  of  giving  an 
amazing  output.  The  life  of  a  vacuum  tube  is  generally  from 
1000  to  5000  hours,  whereas  a  high-frequency  alternator,  such 
as  the  Alexanderson,  will  last  for  many  years. 

It  is  entirely  beyond  the  scope  of  this  book  to  explain  the 
actual  details  of  a  wireless-telephone  transmitting  station. 
However,  the  method  used  at  present  in  high-power  long- 
distance .transmission  is  indicated  in  Fig.  471  and  may  be 
outlined  as  follows:  Air  vibrations  produced  by  the  voice 


ELECTRICAL  RADIATIONS 


435 


make  variations  in  the  current  of  the  primary  circuit  of  the 
telephone  transmitter  (§  376).  This  induces  corresponding 
E.  M.F.'s  in  the  secondary  circuit,  which  impresses  audio- 
frequency variations  of  potential  upon  the  grid  of  a  vacuum- 
tube  modulator.  The  resulting  changes  of  audio  frequency 
in  the  current  of  the  plate  circuit  of  the  modulator  corre- 
spondingly affect  the  output  of  the  high-frequency  oscil- 
lation generator.  This  modulated  radio-frequency  output  is 


Three-electrode  vacuum-tube 
high-frequency  oscillation  generator 


\/4.eri 


Telephone 
Transmitter 


Bank  of 
power -tube  amplifiers 


erial 


Oscillation 
Transformer 


Ground 


Vacuum-tube  modulator 


FIG.  471.    High-power  long-distance  wireless-telephone  transmitting  station 

amplified  by  a  bank  of  three-electrode  power  tubes  and  is 
then  delivered  to  the  aerial  through  an  oscillation  trans- 
former. In  broadcasting  stations  (see  opposite  p.  429)  a 
weaker  and  somewhat  simpler  arrangement  of  tubes  is  used. 

NOTE.  The  following  reference  books  will  prove  helpful  to  teachers  and 
to  those  pupils  who  desire  a  more  complete  understanding  of  "wireless  "  : 
(1)  BUCHER,  Practical  Wireless  Telegraphy,  Wireless  Press,  326  Broad- 
way, New  York  City  ;  (2)  GOLDSMITH,  Radio  Telephony,  Wireless  Press, 
326  Broadway,  New  York  City  ;  (3)  HAUSMANN  and  others,  Radio  Phone 
Receiving,  Van  Nostrand  Co.,  8  Warren  St.,  New  York  City  ;  (4)  MORE- 
CROFT,  Principles  of  Radio  Communication,  John  Wiley  and  Sons,  432 
Fourth  Ave.,  New  York  City;  (5)  SCOTT-TAGGART,  Thermionic  Tubes  in 
Radio  Telegraphy  and  Telephony,  Wireless  Press,  326  Broadway,  New 
York  City ;  (6)  Elementary  Principles  of  Radio  Telegraphy  and  Teleph- 
ony (Radio  Communication  Pamphlet  1),  79  pages,  illustrated,  10  cents. 
Superintendent  of  Documents,  Government  Printing  Office,  Washington, 
D.C.,  1922. 


436  INVISIBLE  RADIATIONS 

Although  transoceanic  telephonic  communication  has  been  suc- 
cessfully and  repeatedly  accomplished  (see  opposite  p.  441), 
no  regular  service  for  such  communication  has  yet  been 
established. 

495.  The  electromagnetic  theory  of  light.     The  study  of 
electromagnetic  radiations,  like  those  discussed    in  the  pre- 
ceding paragraphs,  has  shown  not  only  that  they  have  the 
speed   of   light  but  that  they   are   reflected,   refracted,  and 
polarized,  —  in  fact,  that  they  possess  all  the  properties  of  light 
waves,  the  only  apparent  difference   being   in   their  greater 
wave  length.    Hence  modern  physics  regards  light  as  an  electro- 
magnetic phenomenon ;  that  is,  light  waves  are  thought  to  be 
generated  by  the  oscillations  of  the  electrically  charged  parts 
of  the  atoms.    It  was  as  long  ago  as  1864  that  Clerk-Maxwell, 
(see  opposite  p.  102),  of   Cambridge,  England,,  one  of   the 
world's  most  brilliant  physicists  and  mathematicians,  showed 
that  it  ought  to  be  possible  to  create  ether  waves  by  means 
of  electrical  disturbances.    But  the  experimental  confirmation 
of  his  theory  did  not  come  until  the  time  of  Hertz's  experi- 
ments (1888).    Maxwell  and  Hertz  together,  therefore,  share 
the  honor  of  establishing  the  modern  electromagnetic  theory 
of  light. 

CATHODE  AND  RONTGEN  RAYS 

496.  The  electric  spark  in  partial  vacua.   Let  a  and  b  (Fig.  472) 

foe  the  terminals  of  an  induction  coil  or  static  machine ;  e  and/",  electrodes 
sealed  into  a  glass  tube  60  or  80 
centimeters    long ;    g,  a  rubber 
tube  leading  to  an  air  pump  by 
which    the    tube    may    be    ex- 
hausted.   Let  the  coil  be  started 
before  the  exhaustion  is  begun. 
A  spark  will  pass  between  a  and       FlG  4?2     Discharge  in  partial  vacua 
6,  since  ab  is  a  very  much  shorter 

path  than  ef.  Then  let  the  tube  be  rapidly  exhausted.  When  the  pres- 
sure has  been  reduced  to  a  few  centimeters  of  mercury,  the  discharge 


CATHODE  AKD  KONTGEN  RAYS      437 

will  be  seen  to  choose  the  long  path  ef  in  preference  to  the  short  path  ab, 
thus  showing  that  an  electrical  discharge  takes  place  more  readily  through  a 
partial  vacuum  than  through  air  at  ordinary  pressures. 

When  the  spark  first  begins  to  pass  between  e  and /it  will 
have  the  appearance  of  a  long  ribbon  of  crimson  light.  As 
the  pumping  is  continued  this  ribbon  will  spread  out  until 
the  crimson  glow  fills  the  whole  tube.  Ordinary  so-called 
Geissler  tubes  are  tubes  precisely  like  the  above  except  that 
they  are  usually  twisted  into  fantastic  shapes  and  are  some- 
times surrounded  with  jackets  containing  colored  liquids, 
which  produce  pretty  color  effects. 

497.  Cathode  rays.  When  a  tube  like  the  above  is  exhausted 
to  a  very  high  degree,  say,  to  a  pressure  of  about  .001  milli- 
meter of  mercury,  the  character  of  the  discharge  changes 
completely.  The  glow  almost  entirely  disappears  from  the 
residual  gas  in  the  tube,  and  certain  invisible  radiations  called 
cathode  rays  are  found  to  be  emitted  by  the  cathode  (the 
terminal  of  the  tube  which  is  connected  to 
the  negative  terminal  of  the  coil  or  static 
machine).  These  rays  manifest  themselves, 
first,  by  the  brilliant  fluorescent  effects  which 
they  produce  in  the  glass  walls  of  the  tube, 
or  in  other  substances  within  the  tube  upon 
which  they  fall;  second,  by  powerful  heat- 
ing effects ;  and  third,  by  the  sharp  shadows 
which  they  cast. 

Thus,  if  the  negative  electrode  is  concave,  as  in 
Fig.  473,  and  a  piece  of  platinum  foil  is  placed  at 
the  center  of  the  sphere  of  which  the  cathode  is  a 
portion,  the  rays  will  come  to  a  focus  upon  a  small 
part  of  the  foil  and  will  heat  it  white-hot,  thus  showing  that  the  rays, 
whatever  they  are,  travel  out  in  straight  lines  at  right  angles  to  the 
surface  of  the  cathode.  Tnis  may  also  be  shown  nicely  by  an  ordi- 
nary bulb  of  the  shape  shown  in  Fig.  475.  If  the  electrode  A  is  made 
the  cathode  and  B  the  anode,  a  sharp  shadow  of  the  piece  of  platinum 


438 


INVISIBLE  RADIATIONS 


in  the  middle  of  the  tube  will  be  cast  on  the  wall  opposite  to  A,  thus 
showing  that  the  cathode  rays,  unlike  the  ordinary  electric  spark,  do 
not  pass  between  the  terminals  of  the  tube,  but  pass  out  in  a  straight 
line  from  the  cathode  surface. 

498.  Nature  of  the  cathode  rays.    The  nature  of  the  cathode 
rays  was  a  subject  of  much  dispute  between  the  years  1875, 
when  they  first  began  to  be  carefully  studied,  and  1898.    Some 
thought   them  to   be   streams  of  .  negatively          , 
charged  particles  shot  off   with  great  speed 
from  the  surface  of  the  cathode,  while  others 
thought   they    were    waves    in   the  ether, — 
some  sort  of  invisible  light.    The  following 
experiment  furnishes  very  convincing  evidence 
that  the  first  view  is  correct. 


NP  (Fig.  474)  is  an  exhausted  tube  within  which 
has  been  placed  a  screen  sf  coated  with  some  sub- 
stance like  zinc  sulphide,  which  fluoresces  brilliantly 
when  the  cathode  rays  fall  upon  it;  mn  is  a  mica 
strip  containing  a  slit  s.  This  mica  strip  absorbs  all 
the  cathode  rays  which  strike  it;  but  those  which 
pass  through  the  slit  s  travel  the  full  length  of  the 
tube,  and  although  they  are  themselves  invisible,  yIG  474  Deflec- 
their  path  is  completely  traced  out  by  the  fluores-  tion  of  cathode 
cence  which  they  excite  upon  sf  as  they  graze  along  rays  by  a  magnet 
it.  If  a  magnet  M  is  held  in  the  position  shown,  the 
cathode  rays  will  be  seen  to  be  deflected,  and  in  exactly  the  direction 
to  be  expected  if  they  consisted  of  negatively  charged  particles.  For  we 
learned  in  §  298,  p.  244,  that  a  moving  charge  constitutes  an  electric 
current,  and  in  §  350,  p.  293,  that  an  electric  current  tends  to  move  in 
an  electric  field  in  the  direction  given  by  the  motor  rule.  On  the  other 
hand,  a  magnetic  field  is  not  known  to  exert  any  influence  whatever  on 
the  direction  of  a  beam  of  light  or  on  any  other  form  of  ether  waves. 

When,  in  1895,  J.  J.  Thomson  (see  opposite  p.  440),  of 
Cambridge,  England,  proved  that  the  cathode  rays  were  also 
deflected  by  electric  charges,  as  was  to  be  expected  if  they 
consist  of  negatively  charged  particles,  and  when  Perrin  in 


CATHODE  AND  KONTGEN  BAYS       439 

Paris  had  proved  that  they  actually  impart  negative  charges 
to  bodies  on  which  they  fall,  all  opposition  to  the  projected- 
particle  theory  was  abandoned.  The  mass  and  speed  of  these 
particles  are  computed  from  their  deflectibility  in  magnetic 
and  electric  fields. 

Cathode  rays  are  then  to-day  universally  recognized  as  streams 
of  electrons  shot  off  from  the  surface  of  the  cathode  with  speeds 
which  may  reach  the  stupendous  value  of  100,000  miles  per  second. 

499.  X  rays.  It  was  in  1895  that  Rontgen  (see  opposite 
p.  446)  first  discovered  that  wherever  the  cathode  rays  im- 
pinge upon  the  walls  of  a  tube,  or  upon  any  obstacles  placed 
inside  the  tube,  they  give  rise  to  another  type  of  invisible 
radiation  which  is  now  ...,«<*H..I,,(,,... 

known  under  the  name 
of  X  rays  or  Rontgen 
rays.  In  the  ordinary 
X-ray  tube  (Fig.  475) 
a  thick  piece  of  plati- 
num P  is  placed  in  the 

FIG.  475.  An  X-ray  bulb 
center  to  serve  as  a  tar- 
get for  the  cathode  rays,  which,  being  emitted  at  right  angles 
to  the  concave  surface  of  the  cathode  (7,  come  to  a  focus  at 
a  point  on  the  surface  of  this  plate.   This  is  the  point  at  which 
the  X  rays  are  generated  and  from  which  they  radiate  in  all 
directions.    The  target  P  is  sometimes  made  of  a  heavy  piece 
of  tungsten. 

In  order  to  convince  one's  self  of  the  truth  of  this  statement  it  is  only 
necessary  to  observe  an  X-ray  tube  in  action.  It  will  be  seen  to  be 
divided  into  two  hemispheres  by  the  plane  which  contains  the  p1  itinum 
plate  (see  Fig.  475).  The  hemisphere  which  is  facing  the  source  of  the 
X  rays  will  be  aglow  with  a  greenish  fluorescent  light,  while  the  other 
hemisphere,  being  screened  from  the  rays,  is  darker.  By  moving  a 
fluoroscope  (a  zinc-sulphide  screen)  about  the  tube  it  will  be  made  evident 
that  the  rays  which  render  the  bones  visible  come  from  P. 


440  INVISIBLE  RADIATIONS 

500.  Nature  of  X  rays.    While  X  rays  are  like  cathode  rays 
in  producing  fluorescence,  and  also  in  that  neither  of  them  can 
be  refracted  or  polarized,  as  light  is,  they  nevertheless  differ 
from  cathode  rays  in  several  important  respects.    First,  X  rays 
penetrate  many  substances  which  are  quite  impervious  to  cath- 
ode rays;  for  example,  they  pass  through  the  walls  of  the 
glass  tube,  while  cathode  rays  ordinarily  do  not.    Again,  X 
rays  are  not  deflected  either  by  a  magnet  or  by  an  electro- 
static charge,  nor  do  they  carry  electrical  charges  of  any  sort. 
Hence  it  is  certain  that  they  do  not  consist,  like  cathode  rays, 
of  streams  of  electrically  charged  particles. 

It  has  recently  been  shown  that  X  rays  are  extremely  short 
waves  similar  to  but  very  much  shorter  than  light  waves,  and 
of  a  variety  of  lengths.  They  are  so  short  that  the  smoothest 
mirror  we  can  manufacture  is  so  rough  in  comparison  that  it 
diffuses  them.  By  taking  advantage  of  the  regular  arrange- 
ment of  the  molecules  in  the  faces  of  crystals  (mica,  for 
example)  a  kind  of  reflection  known  as  interference  reflection 
is  obtained  when  the  X  rays  strike  at  certain  favorable  angles 
(see  opposite  p.  447  for  X-ray  spectra).  Many  of  the  X  rays 
from  an  ordinary  X-ray  tube  are  so  short  that  it  would  require 
250,000,000  of  them  to  make  an  inch.  This  represents  a  rate 
of  vibration  of  3,000,000,000,000,000,000  per  second. 

501.  X  rays  render  gases  conducting.    One  of  the  notable 
properties  which  X  rays  possess  in  common  with  cathode  rays 
is  the  property  of  causing  any  electrified  body  on  which  they 
fall  to  slowly  lose  its  charge. 

To  demonstrate  the  existence  of  this  property  let  any  X-ray  bulb  be 
set  in  operation  within  5  or  10  feet  of  a  charged  gold-leaf  electroscope. 
The  leaves  at  once  begin  to  fall  together. 

The  reason  for  this  is  that  the  X  rays  shake  loose  electrons 
from  the  atoms  of  the  gas  and  thus  fill  it  with  positively  and 
negatively  charged  particles,  each  negative  particle  being  at  the 
instant  of  separation  an  electron,  and  each  positive  particle  an 


SIR  JOSEPH  THOMSON  (1856-         ) 

Most  conspicuous  figure  in  the  development  of  the  "physics  of  the  electron"; 
born  in  Manchester,  England;  educated  at  Cambridge  University;  Cavendish 
professor  of  experimental  physics  in  Cambridge  since  1884 ;  author  of  a  number  of 
books,  the  most  important  of  which  is  the  "  Conduction  of  Electricity  through 
Gases,"  1903;  author  or  inspirer  of  much  of  the  recent  work,  both  experimental 
and  theoretical,  which  has  thrown  light  upon  the  connection  between  electricity 
and  matter ;  worthy  representative  of  twentieth-century  physics 


The  extraordinary  developments  in  electronics,  in 
which  Sir  Joseph  Thomson  has  played  so  important 
a  part,  have  had  commercial  consequences,  of  which 
the  following  are  perhaps  the  most  significant :  In 
July,  1914,  through  the  development  of  the  DeForest 
audion  into  a  distortionless  telephone  relay  and 
amplifier,  and  the  insertion  of  these  amplifiers  into 
suitably  chosen  places  in  the  telephone  line  between 
San  Francisco  and  New  York,  the  research  physicists 
of  the  Western  Electric  Company  were  able  to  give 
numerous  demonstrations  in  which  audiences  in 
New  York  and  Boston  were  able  to  hear  with  per- 
fect distinctness  the  splashing  of  the  waves  in  the 
San  Francisco  harbor.  By  the  summer  of  1915  the 
same  group  of  men  had  succeeded  in  throwing  tele- 
phonic speech  up  into  the  antennae  of  the  wireless 
station  at  Arlington  with  such  intensity  that  it 
traveled  without  wires  a  third  of  the  way  around 
the  world  and  was  heard  so  distinctly  at  receiving 
stations  in  both  Honolulu  and  Paris  that  even  the 
voices  of  the  speakers  in  Washington  could  be  recog- 
nized. The  illustration  at  the  left  is  a  cut  (1  size) 
of  one  of  the  tubes  with  which  this  extraordinary 
scientific  feat  was  performed.  The  simplified  circuit 
of  a  thermionic  amplifier  is  shown  in  the  diagram 
above.  The  enfeebled  incoming  speech  frequencies 
vary  the  potential  of  the  grid  G,  and  these  varia- 
tions produce  like  variations  in  the  electronic  cur- 
rents flowing  from  the  hot  filament  F  to  the 
plate  P  and  thence  into  the  circuit  in  which  the 
amplified  current  is  needed.  By  the  use  of  these 
devices  the  enormous  energy  amplifications  of 
10,000,000,000,000-fold  have  been  obtained 


AMPLIFIER,  AND  DIAGRAM  OF  RECEIVING  AND  AMPLIFYING  SET 


RADIOACTIVITY  441 

atom  from  which  an  electron  has  been  detached.  Any  charged 
body  in  the  gas  therefore  draws  toward  itself  charges  of  sign 
opposite  to  its  own,  and  thus  becomes  discharged. 

502.  X-ray  pictures.    The  most  striking  property  of  X  rays 
is  their  ability  to  pass  through  many  substances  which  are 
wholly   opaque   to   light,  —  for   example,    cardboard,    wood, 
leather,  and  flesh.    Thus,  if  the  hand  is  held  close  to  a  photo- 
graphic plate  and  then  exposed  to  X  rays,  a  shadow  picture 
of  the  denser  portions  of  the  hand,  that  is,  the  bones,  is  formed 
upon  the  plate.   Opposite  page  359  is  shown  an  X-ray  picture 
of  the  thorax  of  a  living  human  being. 

RADIOACTIVITY 

503.  Discovery  of  radioactivity.    In  1896  Henri  Becquerel 
(see  opposite  p.  446),  in  Paris,  performed  the  following  ex- 
periment.   He  wrapped  a  photographic  plate  in  a  piece  of  per- 
fectly opaque  black  paper,  laid  a  coin  on  top  of  the  paper, 
and  suspended  above  the  coin  a  small  quantity  of  the  mineral 
uranium.    He  then  set  the  whole  away  in  a  dark  room  and 
let  it  stand  for  several  days.    When  he  developed  the  photo- 
graphic plate  he  found  upon  it  a  shadow  picture  of  the  coin 
similar  to  an  X-ray  picture.    He  concluded,  therefore,  that 
uranium  possesses  the  property  of  spontaneously  emitting  rays  of 
some  sort  which  have  the  power  of  penetrating  opaque  objects 
and  of  affecting  photographic  plates,  just  as  X   rays  do.    He 
also  found  that  these  rays,  which  he  called  uranium  rays, 
are  like  X  rays  in  that  they  discharge  electrically  charged 
bodies  on  which  they  fall.    He  found  also  that  the  rays  are 
emitted  by  all  uranium  compounds. 

504.  Radium.    It  was  but  a  few  months  after  Becquerel's 
discovery  that  Madame  Curie  (see  opposite  p.  446),  in  Paris, 
began  an  investigation  of  all  the  known  elements,  to  find 
whether  any  of  the  rest  of  them  possessed  the  remarkable 


442  INVISIBLE  RADIATIONS 

property  which  had  been  found  to  be  possessed  by  uranium. 
She  found  that  one  of  the  remaining  known  elements,  namely, 
thorium,  the  chief  constituent  of  Welsbach  mantles,  is  capable, 
together  with  its  compounds,  of  producing  the  same  effect. 
After  this  discovery  the  rays  from  all  this  class  of  substances 
began  to  be  called  Becquerel  rays,  and  all  substances  which 
emitted  such  rays  were  called  radioactive  substances. 

But  in  connection  with  this  investigation  Madame  Curie 
noticed  that  pitchblende,  the  crude  ore  from  which  uranium- 
is  extracted,  and  which  consists  largely  of  uranium  oxide, 
would  discharge  her  electroscope  about  four  times  as  fast  as 
pure  uranium.  She  inferred,  therefore,  that  the  radioactivity 
of  pitchblende  could  not  be  due  solely  to  the  uranium  con- 
tained in  it,  and  that  pitchblende  must  therefore  contain  some 
hitherto  unknown  element  which  has  the  property  of  emitting 
Becquerel  rays  more  powerfully  than  uranium  or  thorium. 
After  a  long  and  difficult  search  she  succeeded  in  separating 
from  several  tons  of  pitchblende  a  few  hundredths  of  a  gram 
of  a  new  element  which  was  capable  of  discharging  an  electro- 
scope more  than  a  million  times  as  rapidly  as  either  uranium 
or  thorium.  She  named  this  new  element  radium. 

505.  Nature  of  Becquerel  rays.  That  these  rays  which  are 
spontaneously  emitted  by  radioactive  substances  are  not  X 
rays,  in  spite  of  their  srnilarity  in  affecting  a  photographic 
plate,  in  causing  fluorescence,  and  in  discharging  electrified 
bodies,  is  proved  by  the  fact  that  they  are  found  to  be  deflected 
by  both  magnetic  and  electric  fields,  and  by  the  further  fact 
that  they  impart  electric  charges  to  bodies  upon  which  they  fall. 
These  properties  constitute  strong  evidence  that  radioactive 
substances  project  from  themselves  electrically  charged  particles. 

But  an  experiment  performed  in  1899  by  Rutherford  (see 
opposite  p.  446),  then  of  McGill  University,  Montreal,  showed 
that  Becquerel  rays  are  complex,  consisting  of  three  differ- 
ent types  of  radiation,  which  he  named  the  alpha,  beta,  and 


RADIOACTIVITY  443 

gamma  rays.  The  beta  rays  are  found  to  be  identical  in 
all  respects  with  cathode  rays ;  that  is,  they  are  streams  of 
electrons  projected  with  velocities  varying  from  60,000  to 
180,000  miles  per  second.  The  alpha  rays  are  distinguished 
from  these  by  their  very  much  smaller  penetrating  power,  by 
their  very  much  greater  power  of  rendering  gases  conductors, 
by  their  very  much  smaller  deflectibility  in  magnetic  and 
electric  fields,  and  by  the  fact  that  the  direction  of  the  deflec- 
tion is  opposite  to  that  of  the  beta  rays.  From  this  last  fact, 
discovered  by  Rutherford  in  1903,  the  conclusion  is  drawn 
that  the  alpha  rays  consist  of  positively  charged  particles; 
and  from  the  amount  of  their  deflectibility  their  mass  has 
been  calculated  to  be  about  four  times  that  of  the  hydrogen 
atom,  that  is,  about  7400  times  the  mass  of  the  electron, 
and  their  velocity  to  be  about  20,000  miles  per  second. 
Rutherford  and  Boltwood  have  collected  the  alpha  particles 
in  sufficient  amount  to  identify  them  definitely  as  positively 
charged  atoms  of  helium. 

The  difference  in  the  sizes  of  the  alpha  and  beta  particles 
explains  why  the  latter  are  so  much  more  penetrating  than  the 
former,  and  why  the  former  are  so  much  more  efficient  than  the 
latter  in  knocking  electrons  out  of  the  molecules  of  a  gas  and 
rendering  it  conducting.  A  sheet  of  aluminium  foil  .005  centi- 
meter thick  cuts  off  completely  the  alpha  rays  but  offers  practi- 
cally no  obstruction  to  the  passage  of  the  beta  and  gamma  rays. 

The  gamma  rays  are  very  much  more  penetrating  than  even 
the  beta  rays,  and  are  not  at  all  deflected  by  magnetic  or  electric 
fields.  They  are  regular  waves  in  the  ether,  like  X  rays,  only 
shorter ;  and  they  are  commonly  supposed  to  be  produced  by 
the  impact  of  the  beta  particles  on  surrounding  matter. 

506.  Crookes's  spinthariscope.  In  1903  Sir  William  Crookes  (see  oppo- 
site p.  358)  devised  a  little  instrument,  called  the  spinthariscope,  which 
furnishes  very  direct  and  striking  evidence  that  particles  are  being 
continuously  shot  off  from  radium  with  enormous  velocities.  In  the 


444  INVISIBLE  KADIATIONS 

spinthariscope  a  tiny  speck  of  radium  R  (Fig.  476)  is  placed  about  a 

millimeter    above   a   zinc-sulphide    screen    S,  and   the    latter   is    then 

viewed  through  a  lens  L,  which  gives  from  ten  to  r?-**—^^ 

twenty  diameters  magnification.     The  continuous 

soft  glow  of  the  screen,  which  is  all  one  sees  with 

the  naked  eye,  is  resolved  by  the  lens  into  hundreds 

of  tiny   flashes   of   light.     The  appearance   is   as 

though  the  screen  were  being  fiercely  bombarded 

by  an  incessant  rain  of    projectiles,  each  impact 

being  marked  by  a  flash  of  light,  just  as  sparks  fly 


from  a  flint  when  struck  with  steel.    The  experi-    pIG-  473.  Crookes's 
ment  is  a  very  beautiful  one,  and  it  furnishes  very         spinthariscope 
direct    and    convincing    evidence    that   radium   is 

continually  projecting  particles  from  itself  at  stupendous  speeds.  The 
flashes  are  due  to  the  impacts  of  the  alpha,  not  the  beta,  particles 
against  the  zinc-sulphide  screen. 

A  mixture  composed  of  a  radium  compound  and  zinc  sulphide  glows 
constantly  and  is  used  for  the  dials  of  airplane  instruments,  compasses, 
and  watches,  as  well  as  on  gun  sights,  making  them  visible  for  night  use. 

507.  The  disintegration  of  radioactive  substances.  Whatever 
be  the  cause  of  this  ceaseless  emission  of  particles  exhibited 
by  radioactive  substances,  it  is  certainly  not  due  to  any  ordi- 
nary chemical  reactions;  for  Madame  Curie  showed,  when  she 
discovered  the  activity  of  thorium,  that  the  activity  of  all  the 
radioactive  substances  is  simply  proportional  to  the  amount 
of  the  active  element  present,  and  has  nothing  whatever  to  do 
with  the  nature  of  the  chemical  compound  in  which  the  ele- 
ment is  found.  Furthermore,  radioactivity  has  been  found  to 
be  independent  of  all  physical  as  well  as  chemical  conditions. 
The  lowest  cold  or  greatest  heat  does  not  appear  to  affect  it 
in  the  least.  Radioactivity,  therefore,  is  as  unalterable  a 
property  of  the  atoms  of  radioactive  substances  as  is  weight 
itself.  It  is  now  known  that  the  atoms  of  radioactive  sub- 
stances are  slowly  disintegrating  into  simpler  atoms.  Uranium 
and  thorium  have  the  heaviest  atoms  of  all  the  elements.  For 
some  unknown  reason  they  seem  not  infrequently  to  become 


EADIOACTIVITY  445 

unstable  and  project  off  a  part  of  their  mass.  This  projected 
mass  is  the  alpha  particle.  What  is  left  of  the. atom  after 
the  explosion  is  a  new  substance  with  chemical  properties 
different  from  those  of  the  original  atom.  This  new  atom  is, 
in  general,  also  unstable  and  breaks  down  into  something 
else.  This  process  is  repeated  over  and  over  again  until 
some  stable  form  of  atom  is  reached.  Somewhere  in  the 
course  of  this  atomic  catastrophe  some  electrons  leave  the 
mass;  these  are  beta  rays. 

According  to  this  point  of  view,  which  is  now  generally 
accepted,  radium  is  simply  one  of  the  stages  in  the  disintegra- 
tion of  the  uranium  atom.  The  atomic  weight  of  uranium  is 
238.2;  that  of  radium,  about  226;  that  of  helium,  4.00. 
Radium  would  then  beuranium  after  the  latter  has  lost  3  helium 
atoms.  The  further  disintegration  of  radium  through  four 
additional  transformations  has  been  traced.  It  has  been  con- 
jectured that  the  fifth  and  final  product  is  lead.  If  we  subtract 
8  x  4.00  from  238.2,  we  obtain  206.2,  which  is  very  close  to 
the  accepted  value  for  lead,  namely,  207.2.  In  a  similar  way 
six  successive  stages  in  the  disintegration  of  the  thorium  atom 
(atomic  weight,  232.4)  have  been  found,  but  the  final  product 
is  unknown. 

508.  Energy  stored  up  in  the  atoms  of  the  elements.  In 
1903  the  two  Frenchmen,  Curie  and  Labord,  made  an  epoch- 
making  discovery.  It  was  that  radium  is  continually  evolv- 
ing heat  at  the  rate  of  about  one  hundred  calories  per  gram 
per  hour.  More  recent  measurements  have  given  one  hundred 
eighteen  calories.  This  result  was  to  have  been  anticipated 
from  the  fact  that  the  particles  which  are  continually  flying 
off  from  the  disintegrating  radium  atoms  subject  the  whole 
mass  to  an  incessant  internal  bombardment  which  would  be 
expected  to  raise  its  temperature.  This  measurement  of  the 
exact  amount  of  heat  evolved  per  hour  enables  us  to  estimate 
how  much  heat  energy  is  evolved  in  the  disintegration  of  one 


446  INVISIBLE  RADIATIONS 

gram  of  radium.  It  is  about  two  thousand  million  calories,  — 
fully  three  hundred  thousand  times  as  much  as  is  evolved 
in  the  combustion  of  one  gram  of  coal.  Furthermore,  it  is 
not  impossible  that  similar  enormous  quantities  of  energy  are 
locked  up  in  the  atoms  of  all  substances,  existing  there  per- 
haps in  the  form  of  the  kinetic  energy  of  rotation  of  the 
electrons.  The  most  vitally  interesting  question  which  the 
physics  of  the  future  has  to  face  is,  Is  it  possible  for  man  to 
gain  control  of  any  such  store  of  subatomic  energy  and  to  use 
it  for  his  own  ends  ?  Such  a  result  does  not  now  seem  likely 
or  even  possible  ;  and  yet  the  transformations  which  the  study 
of  physics  has  wrought  in  the  world  within  a  hundred  years 
were  once  just  as  incredible  as  this.  In  view  of  what  physics 
has  done,  is  doing,  and  can  yet  do  for  the  progress  of  the 
world,  can  anyone  be  insensible  either  to  its  value  or  to  its 
fascination  ? 

QUESTIONS  AND  PROBLEMS 

1.  Why  is  it  necessary  to  use  a  rectifying  crystal  or  an  audion  in 
series  with  a  telephone  receiver  to  detect  electric  waves? 

2.  Explain  why  an  electroscope  is  discharged  when  a  bit  of  radium 
is  brought  near  it. 

3.  The  wave  length  of  the  shortest  X  rays  is  about  .00000001  cm. 
How  many  times  greater  is  the  wave  length  of  green  light? 


WILLIAM  CONRAD  RONTGEN, 

MUNICH 
Discoverer  of  X  rays 


ANTOINE  HENRI  BECQUEREL, 
PARIS 

Discoverer  of  radioactivity 


MADAME  CURIE,  UNIVERSITY 

OF  PARIS 
Discoverer  of  radium 


E.  RUTHERFORD,  CAMBRIDGE 
UNIVERSITY  (ENGLAND) 

Discoverer  of  radioactive  trans- 
formations 


A  GROUP  OF  MODERN  PHYSICISTS 


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APPENDIX 


SUPPLEMENTARY  QUESTIONS  AND  PROBLEMS 

CHAPTER  I.  1.  A  new  lead  pencil  is  7  in.  long.  How  many  centi- 
meters long  is  it? 

2.  From  the  bed  rock  upon  which  the  Woolworth  Building  in  New 
York  rests  to  the  top  of  the  tower  is  278.3  m.    How  many  feet  is  it? 

3.  The  wing  spread  of  the  NC-4  is  126  ft.    How  many  meters  is  it? 

4.  How  many  kilograms  are  there  in  the  16-pound  shot? 

5.  Name  three  uses  made  of  lead  because  of  its  great  density,  and 
two  uses  of  cork  due  to  its  small  density. 

6.  A  flask  held  2520  g.  of  glycerin  when  filled.    What  was  the  capac- 
ity of  the  flask  in  liters?    (See  table  of  densities,  p.  9.) 

CHAPTER  II.  1.  A  standpipe  100ft.  high  is  filled  with  water.  Find 
the  pressure  at  the  bottom  in  pounds  per  square  foot  and  in  pounds  per 
square  inch.  ca 

2.  Deep-sea  fish  have  been  caught  in  nets  at  a  depth 
of  a  mile.    How  many  pounds  pressure  are  there  to  the 
square    inch   at  this    depth?     (Specific   gravity  of  sea 
water  =  1.026.) 

3.  If  the  pressure  at  a  tap  on  the  first  floor  reads 
80  Ib.  per  square  inch,  and  at  a  tap  two  floors  above, 
68  Ib.,  what  is  the  difference  in  feet  between  the  levels 
of  the  two  taps? 

4.  Find  the  total  force  against  the  gate  of  a  lock  if 
its  width  is  60  ft.  and  the  depth  of  the  water  20  ft.  Will 
it  have  to  be  made  stronger  if  it  holds  back  a  lake  than 
if  it  holds  back  a  small  pond  ? 

5.  Fig.  477  represents  an  instrument  commonly  known 
as  the  hydrostatic  bellows.    If  the  base  C  is  20  in.  square 
and  the  tube  is  filled  with  water  to  a  depth  of  5  ft.  above 
the  top  of  C,  what  is  the  value  of  the  weight  which  the 
bellows  can  support  ? 

6.  A  hydraulic  press  having  a  piston  1  in.  in  diameter  exerts  a  force 
of  10,000  Ib.  when  10  Ib.  are  applied  to  this  piston.    What  is  the  diam- 
eter of  the  large  piston  ? 

447 


FIG.  477 

Hydrostatic 
bellows 


448 


APPENDIX 


B  = 


7.  A  floating  dock  is  shown  in  Fig.  478.    When  the  chambers  c  are 
filled  with  water,  the  dock  sinks  until  the  water  line  is  at  A.   The  vessel 
is  then  floated  into  the  dock.   As  soon  as  it  is  in  place,  the  water  is 
pumped  from  the  chambers  until  the 

water  line  is  as  low  as  B.  Work- 
men can  then  get  at  all  parts  of  the 
bottom.  If  each  of  the  chambers  is 
10  ft.  high  and  10  ft.  wide,  what 
must  be  the  length  of  the  dock  if 
it  is  to  be  available  for  the  Beren- 
garia  (Cunard  Line),  of  50,000  tons' 
weight? 

8.  If    each    boat   of    a   pontoon 

bridge  is  100  ft.  long  and  75  ft.  wide  at  the  water  line,  how  much  will 
it  sink  when  a  locomotive  weighing  100  tons  passes  over  it? 

9.  What  must  be  the  specific  gravity  of  a  liquid  in  which  a  body 
having  a  specific  gravity  of  6.8  will  float  with  half  its  volume  submerged  V 

10.  A  block  of  wood  10  in.  high  sinks  6  in.  in  water.   Find  the  density 
of  the  wood. 

11.  If  this  block  sank  7  in.  in  oil,  what  would  be  the  density  of  the  oil '( 

12.  A  graduated  glass  cylinder  contains  190  cc.  of  water.   An  egg 
weighing  40  g.  is  dropped  into  the  glass ;  it  sinks  to  the  bottom  and 
xaises  the  water  to  the  225-cc.  mark.    Find  the  density  of  the  egg. 


FIG.  478.  Floating  dock 


CHAPTER  III.   1.  Explain  the  process  of  making  air  enter  the  lungs; 
of  making  lemonade  rise  in  a  straw. 

2.  If  a  circular  piece  of  wet  leather  having  a  string  attached  to  the 
middle  is  pressed  down  on  a  flat,  smooth  stone,  as  in  Fig.  479,  the  latter 
may  often  be  lifted  by  pulling  on  the  string.    Is  it  pulled  up  or  pushed 
up  ?   Explain. 

3.  Make  a  labeled  drawing  of  a  simple  Torricellian 
barometer,  naming  all  the  parts  in  the  diagram. 

4.  The  body  of  the  average  man  has  15  sq.  ft.  of  sur- 
face.   What  is  the  total  force  of  the  atmosphere  upon 
Mm  ?   Why  is  he  unconscious  of  this  crushing  force  ? 

5.  If  the    variation   of   the    height  of    a   mercury 
barometer  is  2  in.,  how  far  did  the  image  rise  and  fall 
in  Otto  von  Guericke's  water  barometer  ?    (See  §  42.) 

6.  What  is  Boyle's  law  ?  A  mass  of  air  3  cc.  in  volume  is  introduced 
into  the  space  above  a  barometer  column  which  originally  stands  at 
760  mm.    The  column  sinks  until  it  is  only  570  mm.  high.    Find  the 
Tolume  now  occupied  by  the  air. 


FIG.  479 


QUESTIONS  AND  PEOBLEMS  449 

7.  There  is  a  pressure  of  80  cm.  of  mercury  on  1000  cc.  of  gas. 
What  pressure  must  be  applied  to  reduce  the  volume  to  600  cc.  if  the 
temperature  is  kept  constant? 

8.  Pressure  tests  for  boilers  or  steel  tanks  of  any  kind  are  always 
made  by  filling  them  with  water  rather  than  with  air.    Why  ? 

9.  If  the  water  within  a  diving  bell  is  at  a  depth  of  1033  cm.  beneath 
the  surface  of  a  lake,  what  is  the  density  of  the  air  inside  if  at  the  sur- 
face the  density  of  air  is  .0013  and  its  pressure  76  cm.  ?    What  would 
be  the  reading  of  a  barometer  within  the  bell  ? 

10.  If  a  diver  descends  to  a  depth  of  100  ft.,  what  is  the  pressure  to 
which  he  is  subjected?    What  is  the  density  of  the  air  in  his  suit,  the 
density  at  the  surface  where  the  pressure  is  75  cm.  being  .0012?  (Assume 
the  temperature  to  remain  unchanged.) 

11.  How  many  of  the  laws  of  liquids  and  gases  do  you  find  illustrated 
in  the  experiment  of  the  Cartesian  diver? 

12.  Pascal  proved  by  an  experiment  that  a  siphon  would  not  run  if 
the  bend  in  the  arm  were  more  than  34  ft.  above  the  upper  water  level. 
He  made  it  run,  however,  by  inclining  it  sidewise  until  the  bend  was 
less  than  34  ft.  above  this  level.    Explain. 

13.  How  high  will  a  lift  pump  raise  water  if  it  is  located  upon  the 
side  of  a  mountain  where  the  barometer  reading  is  71  cm.? 

14.  Find    the    lifting   power    of    a  kite   balloon  whose  capacity  is 
37,000  cu.  ft.,  the  lifting  power  of  the  gas  being  64.4  Ib.  per  1000  cu.  ft. 
and  the  weight  of  the  balloon,  cordage,  car,  and  observer  being  1300  Ib. 

CHAPTER  IV.  1.  WThy  does  a  confined  body  of  gas  exert  pressure 
inversely  proportional  to  its  volume  ? 

2.  A  lump  of  copper  sulphate  placed  at  the  bottom  of  a  graduate 
filled  with  water  will  dissolve  and  very  slowly  pass  upward,  although 
a  copper-sulphate  molecule  is  many  times  heavier  than  a  water  molecule. 
Explain. 

CHAPTER  V.  1.  An  airplane  which  flies  in  still  air  with  a  velocity  of 
120  mi.  per  hour  is  flying  in  a  wind  whose  velocity  is  60  mi.  per  hour 
toward  the  east.  Find  the  actual  velocity  of  the  airplane  and  the 
direction  of  its  motion  when  headed  north ;  east ;  south ;  west. 

2.  Represent  graphically  a  force  of  30  Ib.  acting  southeast  and  a 
force   of   40  Ib.  acting   southwest   at  the   same   point.    What    will    be 
the  magnitude  of   the   resultant,  and    what  will  be    its    approximate 
direction? 

3.  Two  concurrent  forces,  each  of  50  Ib.,  act  at  an  angle  of  60°  with 
each  other.    Find  the  resultant  graphically. 


450  APPENDIX 

4.  A  child  weighing  100  Ib.  sits  in  a  swing.    The  swing  is  drawn 
aside  and  held  in  equilibrium  by  a  horizontal  force  of  40  Ib.    Find  the 
tension  in  each  of  the  two  ropes  of  the  swing. 

5.  Four  clothes  posts  were  arranged  to  form  a  square.    A  clothes- 
line was  drawn  around    the  outside  of    the  posts  with    a    force  of 
GO  Ib.     With  what  force    is  each    post   drawn   toward   the  center  of 
the   square  ? 

6.  A  man  weighing  150  Ib.    stood   at  the  middle  of  a  tight-rope 
whose  two  parts  were  each  50  ft.  long.    What  was  the  tension  on  the 
parts  of  the  rope,  the  weight  of  the  man  depressing  the  center  of  the 
rope  1  ft.? 

7.  A  boy  pulls  a  loaded  sled  weighing  200  Ib.  up  a  hill  which  rises 
1  ft.  in  5  measured  along  the  slope.    Neglecting  friction,  how  much  force 
must  he  exert? 

8.  A  cask  weighing  100  Ib.  is  held  at  rest  upon  an  inclined  plank 
8  ft.  long  and  3  ft.  high.    By  the  resolution-and-proportion  method  find 
the  component  of  its  weight  that  tends  to  break  the  plank. 

9.  What  force  will  be  required  to  support  a  50-lb.  ball  on  an  inclined 
plane  of  which  the  length  is  10  times  the  height? 

10.  A  boy  is  able  to  exert  a  force  of  75  Ib.    Neglecting  friction,  how 
long  an  inclined  plane  must  he  have  in  order  to  push  a  truck  weighing 
350  Ib.  up  to  a  doorway  3  ft.  above  the  ground? 

11.  Could  a  kite  be  flown  from  an  automobile  when  there  is  no 
wind?    Explain. 

12.  Why  is  it  unsafe  to  stand  up  in  a  canoe? 

13.  If  a  lead  pencil  is  balanced  on  its  point  on  the  finger,  it  will  be 
in  unstable  equilibrium,  but  if  two  knives  -are  stuck  into  it,  as  in  Fig.  480, 
it  will  be  in  stable  equilibrium.    Why? 

14.  Why  does  a  man  lean  forward  when  he  climbs 
a  hill? 

15.  A   boy  dropped  a  stone  from  a  bridge  and 
noticed  that  it  struck  the  water  in  just  3  sec.    How 
fast  was  it  going  when  it  struck?    How  high  was 
the  bridge  above  the  water  ? 

16.  If  a  body  sliding  without  friction  down  an 
inclined  plane  moves  40  cm.  during  the  first  second 
of  its  descent,  and  if  the  plane  is  500  cm.  long  and 
40.8  cm.  high,  what  is  the  value  of  </?   (Remember 

that  the  acceleration  down  the  incline  is  simply  the  ^ 

component  (§  80)  of  g  parallel  to  the  incline.) 

17.  A  ball  shot  straight  upward  near  a  pond  was  seen  to  strike  the 
water  in  10  sec.    How  high  did  it  rise  ?   What  was  its  initial  speed? 


QUESTIONS  AND  PEOBLEMS  451 

18.  A  trolley  car  moving  from  rest  with  uniform  acceleration  acquired 
a  velocity  of  10  mi.  per  hour  in  15  sec.    What  was  the  acceleration  and 
the  distance  traversed? 

19.  A  bombing  airplane  is  flying  60  mi.  per  hour  in  still  air  at  a  height 
of  1000  ft.    In  order  to  score  a  "  bull's-eye,"  at  what  distance  in  advance 
of  the  target  must  the  bomb  be  let  go  ? 

20.  A  rifle  weighing  5  Ib.  discharges  a  1-oz.  bullet  with  a  velocity  of 
1000  ft.  per  second.    What  will  be  the  velocity  of  the  rifle  in  the  opposite 
direction  ? 

21.  A  steamboat  weighing  20,000  metric  tons  is  being  pulled  by  a 
tug  which  exerts  a  pull  of  2  metric  tons.    (A  metric  ton  is  equal  to 
1000  kg.)     If  the  friction  of  the  water  were  negligible,  what  velocity 
would  the  boat  acquire  in  4  min.?     (Reduce  mass  to  grams,  force  to 
dynes,  and  remember  that  F  =  mv/t.') 

22.  If  a  train  of  cars  weighs  200  metric  tons,  and  the  engine  in  pull- 
ing 5  sec.  imparts  to  it  a  velocity  of  2  m.  per  second,  what  is  the  pull  of 
the  engine  in  metric  tons? 

CHAPTER  VI.  1.  WThat  must  be  the  cross  section  of  a  wire  of  copper 
if  it  is  to  have  the  same  tensile  strength  (that  is,  break  with  the  same 
weight)  as  a  wire  of  iron  1  sq.  mm.  in  cross  section?  (See  §107.) 

2.  How  many  times  greater  must  the  diameter  of  one  wire  be  than 
that  of  another  of  the  same  material  if  it  is  to  have  five  times  the  tensile 
strength  ? 

3.  If  the  position  of  the  pointer  on  a  spring  balance  is  marked 
when  no  load  is  on  the  spring,  and  again  when  the  spring  is  stretched 
with  a  load  of  10  g.,  and  if  the  space  between  the  two  marks  is  then 
divided  into  ten  equal  parts,  will  each  of  these  parts  represent  a  gram  ? 
Why? 

4.  A  wire  which  is  twice  as  thick  as  another  of  similar  material 
will  support  how  many  times  as  much  weight? 

5.  A  force  of  3  Ib.  stretches  1  mm.  a  wire  that  is  1  m.  long  and  .1  mm. 
in  diameter.    How  much  force  will  it  take  to  stretch  5  mm.  a  wire  of  the 
same  material  4  m.  long  and  .2  mm.  in  diameter? 

6.  Why  does  a  small  stream  of  water  break  np  into  drops  instead 
of  falling  as  a  continuous  thread? 

7.  Give  four  common  illustrations  of  capillary  attraction. 

8.  Explain  the  watering  of  flowers  by  setting  the  pot  in  a  shallow 
basin  of  water. 

9.  Why  does  a  new  and  oily  steel  pen  not  write  well?   Why  is  it 
difficult  to  write  on  oiled  paper? 

10.  Would  mercury  ascend  a  lamp  wick  as  oil  and  water  do? 


452 


APPENDIX 


11.  Why  do  some  liquids  rise  while  others  are  depressed  in  capillary 
tubes? 

12.  If  water  will  rise  32  cm.  in  a  tube  .1  mm.  in  diameter,  how  high 
will  it  rise  in  a  tube  .01  mm.  in  diameter? 

13.  How  can  you  tell  whether  bubbles  which  rise  from  the  bottom  of 
a  vessel  which  is  being  heated  are  bubbles  of  air  or  bubbles  of  steam? 

CHAPTER  VII.  1.  A  woman  in  sweeping  a  rug  moved  the  nozzle  of  a 
vacuum  sweeper  a  total  distance  of  130  ft.,  using  an  average  force  of 
one-half  pound.  How  much  work  did  she  do  ? 

2.  Analyze  several  types  of  manual  labor  and  see  if  the  definition 
(  W  =  Fs)  holds  for  each.   Is  not  F  x  s  the  thing  paid  for  in  every  case  ? 

3.  Explain  the  use  of  the  rider  in  weighing  (see  Fig.  22). 

4.  Two  boys  are   carrying  a  bag 
of  walnuts  at  the  middle   of  a  long 
stick.    Will   it  make  any   difference 
whether  they  walk  close   to  the  bag 
or  farther  away,  so  long  as  each  is  at 
the  same  distance  ? 

5.  If  3  horses  are  to  pull  equally 
on  a  load,  how  should  the  whippletree 
be  designed? 

6.  WThy  is  it  that  a  couple  cannot  be  balanced  by  a  single  force? 

7.  If  the  ball  of  the  float  valve  (Fig.  481)  has  a  diameter  of  10  cm.v 
and  if  the  distance  from  the  center  of  the  ball  to  the  pivot  S  is  20 
times  the  distance  from  S  to  the  pin  P,  with  what  force  is  the  valve 
R  held  shut  when  the  ball  is  half  immersed  ?   Neglect  weight  of  ball. 


FIG.  481.  The  automatic 
float  valve 


FIG.  482.   Yale  lock 
(1),  the  right  key;  (2),  the  wrong  key 

8.  In  the  Yale  lock  (Fig.  482)  the  cylinder  G  rotates  inside  the 
fixed  cylinder  F  and  works  the  bolt  through  the  arm  H.  The  right  key 
raises  the  pins  a',  b',  c',  d't  ef  until  their  tops  are  just  even  with  the  top 
of  G.  What  mechanical  principles  do  you  find  involved  in  this  device  ? 


QUESTIONS  AND  PROBLEMS 


458 


FIG.  483.  Differential 
windlass 


9.  A  lever  is  3  ft.  long.   Where  must  the  fulcrum  be  placed  so  that  a, 
weight  of  300  Ib.  at  one  end  shall  be  balanced  by  50  Ib.  at  the  other  ? 

10.  Two  horses  of  unequal  strength  must 
be  hitched  as  a  team.    The  one  is  to  pull 
360  Ib.,  while  the  other  pulls  288  Ib.    In 
a  doubletree  50  in.   long,  where  must  the 
pin  be  placed  to  permit  an  even  pull? 

11.  In  the    differential    wheel  and  axle 
(Fig.  483)  the  rope  is  wound  in  opposite 
directions  on  two  axles  of  different  diameter. 
For  a  complete  revolution  of  the  axle  the 
weight  is  lifted  by  a  distance  equal  to  one 
half  the  difference  between  the  circumfer- 
ences of  the  two  axles.   If  the  crank  has  a 
radius  of  2  ft.,  the  larger  axle  a  diameter  of 

6  in.,  and  the   smaller  one  a  diameter  of  4  in.,  find  the  mechanical 
advantage  of  the  arrangement.    (See  differential  pulley,  p.  119.) 

12.  With  the  aid  of  Fig.  484  describe  the  process  of  winding  and 
setting  a  watch.   The  rocker  R  is  pivoted  at  S  ;   C  carries  the  mainspring 
and  E  the  hands ;  S.  P.  is  a  light  spring  which  normally  keeps  the 
wheel  .4  in  mesh  with  C.   Pressing 

down  on  P,  however,  releases  A 
from  C  and  engages  B  with  D. 
What  mechanical  principles  do 
you  find  involved  ?  What  happens 
when  M  is  turned  backward  ? 

13.  A  150-lb.  man  runs  up  a  flight 
of  stairs  60  ft.  high  in  10  sec.  What 
is  his  horse  power  while  doing  it? 
How  do  you  account  for  the  result  ? 

14.  A  thousand-barrel  tank  at  a 
mean  elevation  of  50  ft.  is  to  be 
filled  with  water.  How  much  work 
must  be  done  to  fill  it,  assuming  a 
barrel  of  water  to  weigh   260  Ib.  ? 
How  long  would  it  take  a  2-horse- 
power  electric  motor  to  fill  it? 

15.  What  must  be  the  horse  power  of  an  engine  which  is  to  pump 
10,000  1.  of  water  per  second  from  a  mine  150  m.  deep?    (Take  76  kilo- 
gram meters  per  second  =  1  horse  power.) 

16.  A  water  motor  discharges  100  1.  of  water  per  minute  when  fed 
from  a  reservoir  in  which  the  water  surface  stands  50  m.  above  the  level 


FIG.  484.  Winding  and  setting  mech- 
anism of  a  stem-winding  watch 


454  APPENDIX 

of  the  motor.  If  all  of  the  potential  energy  of  the  water  were  transformed 
into  work  in  the  motor,  what  would  be  the  horse  power  of  the  motor  ? 
(The  potential  energy  of  the  water  is  the  amount  of  work  which  would 
be  required  to  carry  it  back  to  the  top  of  the  reservoir.) 

17.  A  rifle  weighing  8.5  Ib.  discharges  a  bullet  weighing  0.4  oz.  with 
a  velocity  of  2600  ft.  per  second.  What  is  the  kinetic  energy  of  the  bullet ; 
the  velocity  of  recoil  of  the  rifle  ;  the  kinetic  energy  of  the  rifle? 

CHAPTER  VIII.  1.  What  fractional  part  of  the  air  in  a  room  passes 
out  when  the  air  in  it  is  heated  from  -15°C.  to  20°C.V  (-15°C.  =  258°  A. ; 
20°C.  -293°  A.) 

2.  If  the  volume  of  a  body  of  gas  at  20°  C.  and  76cm.  pressure  is 
500  cc.,  what  is  its  volume  at  50°C.  and  70cm.  pressure? 

3.  An  automobile  tire  contained  air  under  a  pressure  of  70  Ib.  per 
square  inch  at  a  temperature  of  20°C.   On  being  driven,  the  temperature 
of  the  air  rose  to  35°  C.    What  was  the  increase  in  pressure  within 
the  tire? 

4.  Find  the  density  of  the  air  in  a  furnace  whose  temperature  is 
1000°  C.,  the  density  at  0°C.  being  .001293. 

5.  When  the  barometric  height  is  76  cm.  and  the  temperature  0°C., 
the  density  of  air  is  .001293.    Find  the  density  of  air  when  the  tem- 
perature is  38° C.  and  the  barometric  height  is  73  cm.    Find  the  density 
of  air  when  the  temperature  is  —  40°  C.  and  the  barometric  height  74  cm. 

6.  If  an  iron  steam  pipe  is  60  ft.  long  at  0°C.,  what  is  its  length 
when  steam  passes  through  it  at  100°  C.  ? 

7.  If  iron  rails  are  30  ft.  long,  and  if  the  variation  of  temperature 
throughout  the  year  is  50° C.,  what  space  must  be  left  between  their  ends  ? 

8.  If  the  total  length  of  the  iron  rods  b,  <1,  e,  and  i  in  a  compensated 
pendulum  (Fig.  151)  is  2  m.,  what  must  be  the  total  length  of  the  cop- 
per rods  c  if  the  period  of  the  pendulum  is  independent  of  temperature  ? 

9.  Two  metal  bars,  one  aluminium  and  the  other  steel,  are  both 
100  cm.  long  at  0°C.    How  much  will  they  differ  in  length  at  30°C.? 
(See  table  on  page  140.) 

CHAPTER  IX.    1.  Name  three  uses  and  three  disadvantages  of  friction. 

2.  There  is  a  Pelton  wheel  at  the  Sutro  tunnel  in  Nevada  which  is 
driven  by  water  supplied  from  a  reservoir  2100  ft.  above  the  level  of  the 
motor.    The  diameter  of  the  nozzle  is  about  J  in.,  and  that  of  the  wheel 
but  3  ft,  yet  100  H.  P.  is  developed.    If  the  efficiency  is  80%,  how  many 
cubic  feet  of  water  are  discharged  per  second  ? 

3.  A  turbine  having  an  efficiency  of  80%  was  supplied  with  200  cu.  ft. 
of  water  per  second  at  a  head  of  50  ft.  What  horse  power  was  developed  ? 


QUESTIONS  AND  PROBLEMS  455 

4.  How  many  calories  of  heat  are  generated  by  the  impact  of  a  200- 
kilo  bowlder  when  it  falls  vertically  through  100  m.?    (The  mechanical 
equivalent  of  heat  =  427  g.ni.) 

5.  Thousands  of  meteorites  are  falling  into  the  sun  with  enormous 
velocities  every  minute.   From  a  consideration  of  the  preceding  example 
account  for  a  portion,  at  least,  of  the  sun's  heat. 

6.  The  kinetic  energy  of  mass  motion  of  an  automobile  running 
20  mi.  per  hour  was  37,34-4  ft.  Ib.   In  stopping  this  car  how  many  B.  T.  U. 
were  developed  in  the  brakes  ? 

7.  400  g.  of  aluminium  at  100°  C.  were  dropped  into  500  g.  of  water 
at  20°  C.    The  water  equivalent  of  the  calorimeter  was  40  grams.    Find 
the  resultant  temperature.    (See  table  on  page  160.) 

8.  A  copper  ball  weighing  3  kg.  was  heated  to  a  temperature  of 
100°  C.    When  placed  in  water  at  15°  G.  it  raised  the  temperature  to 
25°  C.    How  many  grams  of  water  were  there  ?   (See  table  on  page  160.) 

9.  100  g.  of  water  at  80°  C.  are  thoroughly  mixed  with  500  g.  of 
mercury  at  0°  C.    What  is  the 'temperature  of  the  mixture? 

10.  A  piece  of  platinum  weighing  10  g.  is  taken  from  a  furnace  and 
plunged  instantly  into  40  g.  of  water  at  10°  C.    The  temperature  of  the 
water  rises  to  24°  C.    What  was  the  temperature  of  the  furnace  ? 

11.  How  many  grams  of  ice-cold  water  must  be  poured  into  a  tum- 
bler weighing  300  g.  to  cool  it  from  60°  C.  to  20°  C.,  the  specific  heat 
of  glass  being  .2  V 

12.  If  you  put  a  20-g.,  silver  spoon  at  20°  C.  into  a  150-cc.  cup  of  tea 
at  70°  C.,  how  much  do  you  cool  the  tea  ? 

13.  Which  would  be  heated  more,  a  lead  or  a  steel  bullet,  if  they  were 
fired  against  a  target  with  equal  speeds  ? 

14.  If  the  specific  heat  of  lead  is  .031  and  the  mechanical  equivalent 
of  a  calorie  427  g.  m.,  through  how  many  degrees  centigrade  will  a 
1000-g.  lead  ball  be  raised  if  it  falls  from  a  height  of  100  m.,  provided 
all  of  the  heat  developed  by  the  impact  goes  into  the  lead  ? 

15.  A  car  weighing  60,000  kilos  slides  down  a  grade  which  is  2  m. 
lower  at  the  bottom  than  at  the  top  and  is  brought  to  rest  at  the  bottom 
by  the  brakes.    How  many  calories  of  heat  are  developed  by  the  friction  ? 

16.  Explain  why  the  cylinder  of  an  automobile-tire  pump  becomes 
hot  when  the  pump  is  being  used.    Why  is  the  air  cooled  as  it  escapes 
from  the  valve  of  an  automobile  tire? 

CHAPTER  X.    1.  What  is  the  temperature  of  a  mixture  of  ice  and 
water  ?    What  determines  whether  it  is  freezing  or  melting  ? 

2.  Why  does  ice  cream  seem  so  much  colder  to  the  teeth  than  ice 
water  ? 


456  APPENDIX 

•=     •; 

3.  If  water  were  like  gold  in  contracting  on  solidification,  what 
would  happen  to  lakes  and  rivers  during  a  cold  winter  ? 

4.  Equal  weights  of  hot  water  and  ice  are  mixed,  and  the  result  is 
water  at  0°  C.   What  was  the  temperature  of  the  hot  water  ? 

5.  Which  is  the  more  effective  as  a  cooling  agent,  100  Ib.  of  ice  at 
0°  C.  or  100  Ib.  of  water  at  the  same  temperature?   Why? 

6.  What  temperature  will  result  from  mixing  10  g.  of  ice  at  0°  C. 
with  200  g.  of  water  at  25°  C.? 

7.  From  what  height  must  a  gram  of  ice  at  0°  C.  fall  in  order  to 
melt  itself  by  the  heat  generated  in  the  impact  ? 

8.  If  dry  air  were  placed  in  a  closed  vessel  when  the  barometer  was 
76  cm.,  and  if  a  dish  of  water  were  then  introduced  within  the  closed 
space,  what  pressure  would  finally  be  attained  within  the  vessel  if  the 
temperature  were  kept  at  18°  C.? 

9.  If  there  were  moisture  on  the  face,  would  fanning  produce  any 
feeling  of  coolness  in  a  saturated  atmosphere  ? 

10.  Would  fanning  produce  any  feeling  of  coolness  if  there  were  no 
moisture  on  the  face  ? 

11.  Explain  the  formation  of  frost  on  the  window  panes  in  winter. 

12.  In  the  fall  we  expect  frost  on  clear  nights  when  the  dew  point  is 
low,  but  not  on  cloudy  nights  when  the  dew  point  is  high.    Can  you  see 
any  reason  why  a  large  deposit  of  dew  should  prevent  the  temperature  of 
the  air  from  falling  very  low  ? 

13.  Why  does  the  distillation  of  a  mixture  of  alcohol  and  water 
always  result  to  some  extent  in  a  mixture  of  alcohol  and  water  ? 

14.  How  much  heat  is  given  up  by  30  g.  of  steam  at  100°  C.  in  con- 
densing to  water  at  the  same  temperature  ? 

15.  A  vessel  contains  300  g.  of  water  at  0°  C.  and  130  g.  of  ice.   If  25  g. 
of  steam  are  condensed  in  it,  what  will  be  the  resulting  temperature  ? 

16.  To  convert  1  g.  of  water  at  0°  C.  into  steam  at  100°  C.  requires 
636  calories.    When  the  boiling  point  of  water  is  100°  C.,  how  many  of 
these  calories  are  used  to  vaporize  the  water?    At  an  elevation  where 
water  boils  at  90°  C.,  how  many  calories  are  required  for  the  vaporization? 
(Specific  heat  of  steam  =  0.5.) 

17.  Bearing  in  mind  that  the  cooler  the  water  the  less  the  kinetic 
agitation  of  its  molecules,  why  should  you  expect  a  larger  result  at  90°  C. 
than  536  calories  ? 

18.  When  the  steam  gauge  of  a  locomotive  records  250  Ib.  per  square 
inch,  the  steam  is  at  a  temperature  of  406°  F.   Explain  how  the  steam 
produces  this  great  pressure. 

19.  If  the  average  pressure  in  the  cylinder  of  a  steam  engine  is  10 
kilos  to  the  square  centimeter,  and  the  area  of  the  piston  is  427  sq.  cm., 


QUESTIONS  AXD  PROBLEMS  457 

how  much  work  is  done  by  the  piston  in  a  stroke  of  length  50  cm.  ? 
How  many  calories  did  the  steam  lose  in  this  operation? 

20.  The  total  efficiency  of  a  certain  600-horse-power  locomotive  is  6%  ; 
8000  calories  of  heat  are  produced  by  the  burning  of  1  g.  of  the  best 
anthracite  coal ;  how  many  kilos  of  such  coal  are  consumed  per  hour 
by  this  engine  ?  (Take  1  H.  P.  =  746  watts  and  1  calorie  per  second 
=  4.2  watts.) 

CHAPTER  XI.  1.  Why  are  the  pipes  that  carry  steam  from  the  boiler 
to  the  radiators  often  covered  with  cellular  asbestos?  Why  is  the  cellular 
structure  an  advantage  ? 

2.  Explain  the  cause  of  the  sea  breeze  which  occurs  in  coast  regions 
on  summer  afternoons. 

3.  Is  the  draft  through  the  fire  of  a  kitchen  range  pushed  through 
or  drawn  through?   Explain. 

4.  Why  should  steam  radiators  be  installed  on  the  cold  side  of  a  room, 
for  example,  near  outside  walls  or  windows? 

5.  Describe  all  the  processes  involved  in  the  transference  of  heat 
energy  from  the  fire  under  the  steam  boiler  in  a  cellar  to  the  rooms  con- 
taining the  radiators. 

CHAPTER  XII.  1.  If  a  bar  magnet  is  floated  on  a  piece  of  cork,  will 
it  tend  to  float  toward  the  north  ?  Why  ? 

2.  The  dipping  needle  is  suspended  from  one  arm  of  a  steel-free 
balance  and  carefully  weighed.   It  is  then  magnetized.    Will  its  apparent 
weight  increase  ? 

3.  When  a  piece  of  soft  iron  is  made  a  temporary  magnet  by  bringing 
it  near  the  N  pole  of  a  bar  magnet,  will  the  end  of  the  iron  nearest  the 
magnet  be  an  N  or  an  S  pole  ? 

4.  To  which  do  isogonic  lines  as  a  rule  correspond  most  nearly,  the 
parallels  or  the  meridians  ? 

5.  Lines  connecting  those  places  on  the  earth  where  the  inclination 
of  the  dipping  needle  is  the  same  are  called  isoclinic  lines.    Do  isoclinic 
lines  in  general  trend  approximately  N  and  S  or  E  and  W? 

6.  With  what  force  will  an  N  magnetic  pole  of  strength  6  attract,  at 
a  distance  of  5  cm.,  an  S  pole  of  strength  1?  of  strength  9  ? 

CHAPTER  XIII.  1.  Why  is  repulsion  between  an  unknown  body  and 
an  electrified  pith  ball  a  surer  sign  that  the  unknown  body  is  electrified 
than  is  attraction? 

2.  If  you  charge  an  electroscope  and  then  bring  your  hand  toward 
the  knob  (not  touching  it),  the  leaves  go  closer  together.  Why? 


458  APPENDIX 

3.  Two  small  spheres  are  charged  with  +  16  and   —  4  units  of  elec- 
tricity.   With  what  force  will  they  attract  each  other  when  at  a  distance 
of  4cm.? 

4.  If  the  two  spheres  of  the  previous  problem  are  made  to  touch  and 
are  then  returned  to  their  former  positions,  with  what  force  will  they 
act  on  each  other  ?    Will  this  force  be  attraction  or  repulsion  ? 

5.  Why  is  the  capacity  of  a  conductor  greater  when  another  con- 
ductor connected  to  the  earth  is  near  it  than  when  it  stands  alone? 

6.  A  Leyden  jar  is  placed  on  a  glass  plate  and  10  units  of  electricity 
placed  on  the  inner  coating.    The  knob  is  then  connected  to  a  gold-leaf 
electroscope.   W'ill  the  leaves  of  the  electroscope  stand  farther  apart  now 
or  after  the  outside  coating  has  been  connected  to  the  earth  ? 

CHAPTER  XIV.    1.  Why  would  an  electromagnet  made  by  winding 
bare  wire  on  a  bare  iron  core  be  worthless  as  a  magnet? 

2.  The  plane  of  a  suspended  loop  of  wire  is  east  and  west.    A  cur- 
rent is  sent  through  it,  passing  from  east  to  west  on  the  upper  side. 
What  will  happen  to  the  loop  if  it  is  perfectly  free  to  turn  ? 

3.  When  a  strong  current  is  sent  through  a  suspended-coil  galva- 
nometer, what  position  will  the  coil  assume  ? 

4.  If  the  earth's  magnetism  is  due  to  a  surface  charge  rotating  with 
the  earth,  must  this  charge  be  positive  or  negative  in  order  to  produce 
the  sort  of  magnetic  poles  which  the  earth  has?    (This  is  actually  the 
present  theory  of  the  earth's  magnetism.) 

5.  Why  must  a  galvanometer  which  is  to  be  used  for  measuring 
voltages  have  a  high  resistance  ? 

6.  Why  is  the  E.  M.  F.  of  a  cell  equal  to  the  P.  D.  of  its  terminals  when 
on  open  circuit?   (Explain  by  reference  to  the  water  analogy  of  §  318.) 

7.  Can  you  prove  from  a  consideration  of  Ohm's  law  that  when 
wires  of  different  resistances  are  inserted  in  series  in  a  circuit,  the  P.  D.'s 
between  the  ends  of  the  various  wires  are  proportional  to  the  resistances 
of  these  wires  ? 

8.  How  long  a  piece  of  No.  30  copper  wire  will  have  the  same 
resistance  as  a  meter  of  No.  30   German-silver  wire  ?     (See  table  of 
specific  resistances,  p.  262.)  '  9 

9.  The  diameter  of  Xo.  20  wire  is  31.96  mils  (1  mil  =  .001  in.)  and 
that  of  No.  30  wire  10.025  mils.     Compare  the  resistances  of  equal 
lengths  of  No.  20  and  No.  30  German-silver  wires. 

10.  What  length  of  No.  30  copper  wire  will  have  the  same  resistance 
as  20  ft.  of  No.  20  copper  wire  ? 

11.  AVhat  length  of  No.  20  German-silver  wire  will  have  the  same 
resistance  as  100  ft.  of  No.  30  copper  wire  ? 


QUESTIONS  AND  PROBLEMS  459 

12.  A  galvanometer  has  a  resistance  of  588  ohms.    Jf  only  one  fiftieth 
of  the  current  in  the  main  circuit  is  to  be  allowed  to  pass  through  the 
moving  coil,  what  must  be  the  resistance  of  the  shunt  ? 

13.  Ten  pieces  of  wire,  each  having  a  resistance  of  5  ohms,  are  con- 
nected in  parallel  (see  Fig.  278).    If  the  junction  a  is  connected  to  one 
terminal  of  a  Daniell  cell  and  b  to  the  other,  what  is  the  total  current 
which  will  flow  through  the  circuit  when  the  E.  M.  F.  of  the  cell  is  1  volt 
and  its  resistance  2  ohrns? 

14.  Jf  a  certain  Daniell  cell  has  an  internal  resistance  of  2  ohms  and 
an  E.  M.  F.  of  1.08  volts,  what  current  will  it  send  through  an  ammeter 
whose  resistance  is  negligible?   What  current  will  it  send  through  a 
copper  wire  of  2  ohms  resistance?   through  a  German-silver  wire  of 
100  ohms  resistance?  • 

15.  A  Daniell  cell  indicates  a  certain  current  when  connected  to  a 
galvanometer  of  negligible  resistance.    When  a  piece  of  No.  20  German- 
silver  wire  is  inserted  into  the  circuit,  it  is  found  to  require  a  length  of 
5  ft.  to  reduce  the  current  to  one  half  its  former  value.    Find  the  resist- 
ance of  the  cell  in  ohms,  No.  20  German-silver  wire  having  a  resistance 
of  190.2  ohms  per  1000  ft. 

16.  A  coil  of  unknown  resistance  is  inserted  in  series  with  a  con- 
siderable length  of  No.  30  German-silver  wire  and  joined  to  a  Daniell 
cell.    When  the  terminals  of  a  high-resistance  galvanometer  are  touched 
to  the  wire  at  points  10  ft.  apart,  the  deflection  is  found  to  be  the 
same  as  when  they  are  touched  across  the  terminals  of  the  unknown 
resistance.    What  is  the  resistance  of  the  unknown  coil?    (See  §  316, 
p.  263.) 

17.  How  do  we  calculate  the  power  consumed  in  any  part  of  an 
electric  circuit  ?   What  horse  power  is  required  to  run  an  incandescent 
lamp  carrying  .5  ampere  at  110  volts? 

18.  An  electric  soldering  iron  allows  5  amperes  to  flow  through  it 
when  connected  to  an  E.  M.  F.  of  110  volts.  What  will  it  cost,  at  12  cents 
per  kilowatt  hour,  to  operate  the  iron  6  hr.  per  day  for  5  da.? 

19.  An  electric  motor  developed  2  horse  power  when  taking  16.5 
amperes  at  110  volts.    Find  the  efficiency  of  the  motor.    (One  horse 
power  =  7-1 G  watts.) 

CHAPTER  XY.  1.  If  the  coil  of  a  sensitive  galvanometer  is  set  to 
swinging  while  the  circuit  through  the  coil  is  open,  it  will  continue 
to  swing  for  a  long  time ;  but  if  the  coil  is  short-circuited,  it  will  come 
to  rest  after  a  very  few  oscillations.  Why?  (The  experiment  may  easily 
be  tried.  Remember  that  currents  are  induced  in  the  moving  coil. 
Apply  Lenz's  law.) 


460  APPENDIX 

2.  Show  that  if  the  reverse  of  Leuz's  law  were  true,  a  motor  once 
started  would  run  of  itself  and  do  work;  that  is,  it  would  furnish  a  case 
of  perpetual  motion. 

3.  If  a  series-wound  dynamo  is  running  at  a  constant  speed,  what 
effect  will  be  produced  on  the  strength  of  the  field  magnets  by  dimin- 
ishing the  external  resistance  and  thus  increasing  the  current?    What 
will  be  the  effect  on  the  E.M.  F.?    (Remember  that  the  whole  current 
goes  around  the  field  magnets.)    (See  §  357.) 

4.  If  a  shunt-wound  dynamo  is  run  at  constant  speed,  what  effect 
will  be  produced  on  the  strength  of  the  field  magnets  by  reducing  the 
external  resistance  ?    What  effect  will  this  have  on  the  E.M.F.? 

5.  In  an  incandescent-lighting  system  the  lamps  are  connected  in 
parallel  across  the  mains.    Every  lamp  which  is  turned  on,  then,  dimin- 
ishes the  external  resistance.    Explain  from  a  consideration  of  Problems 
3  and  4  why  a  compound-wound  dynamo  (Fig.  318)  keeps  the  P.  D. 
between  the  mains  constant. 

6.  When  an  electric  fan  is  first  started,  the  current  through  it  is  much 
greater  than  it  is  after  the  fan  has  attained  its  normal  speed.    Why  ? 

7.  If  the  pressure  applied  at  the  terminals  of  a  motor  is  500  volts, 
and  the  back  pressure,  when  running  at  full  speed,  is  450  volts,  what  is 
the  current  flowing  through  the  armature,  its  resistance  being  10  ohms? 

8.  Two  successive  coils  on  the  armature  of  a  multipolar  alternator 
are  cutting^lines  of  force  which  run  in  opposite  directions.    How  does 
it  happen  that  the  currents  generated  flow  through  the  wires  in  the 
same  direction?    (Fig.  310.) 

9.  A  multipolar  alternator  has  20  poles  and  rotates  200  times  per 
minute.    How  many  alternations  per  second  will  be  produced  in  the 
circuit  ? 

10.  With  the  aid  of  the  dynamo  rule  explain  why,  in  Figs.  313  and 
315,  the  current  in  the  conductors  under  the  north  poles  is  moving 
toward  the  observer  and  that  in  the  conductors  under  the  south  poles 
away  from  the  observer. 

CHAPTER  XVI.  1.  A  bullet  fired  from  a  rifle  with  a  speed  of  1200  ft. 
per  second  is  heard  to  strike  the  target  6  sec.  aftei*wards.  Wrhat  is  the 
distance  to  the  target,  the  temperature  of  the  air  being  20°  C.?  (Let 
x  —  the  distance  to  the  target.) 

2.  A  church  bell  is  ringing  at  a  distance  of  1  mi.  from  one  man 
and  ^  mi.  from  another.     How  much  louder  would  it  appear  to  the 
second  man  than  to  the  first  if  no  reflections  of  the  sound  took  place  ? 

3.  A  stone  is  dropped  into  a  well  200  m.  deep.    At  20°  C.  how  much 
time  will  elapse  before  the  sound  of  the  splash  is  heard  at  the  top? 


QUESTIONS  AND  PROBLEMS  461 

4.  As  a  circular  saw  cuts  into  a  block  of  wood  the  pitch  of  the  note 
given  out  falls  rapidly.    Why  ? 

5.  A  clapper  strikes  a  bell  once  every  two  seconds.    How  far  from 
the  bell  must  a  man  be  in  order  that  the  clapper  may  appear  to  hit  the 
bell  at  the  exact  instant  at  which  each  stroke  is  heard  ? 

6.  The  note  from  a  piano  string  which  makes  300  vibrations  per 
second  passes  from  indoors,  where  the  temperature  is  20°  C.,  to  outdoors, 
where  it  is  0°  C.    What  is  the  difference  in  centimeters  between  the 
wave  lengths  indoors  and  outdoors? 

7.  A  man  riding  on  an  express  train  moving  at  the  rate  of  1  mi. 
per  minute  hears  a  bell  ringing  in  a  tower  in  front  of  him.    If  the  bell 
makes  280  vibrations  per  second,  how  many  pulses  will  strike  his  ear 
per  second,  the  velocity  of  sound  being  1120  ft.  per  second?     (The 
number  of  extra  impulses  received  per  second  by  the  ear  is  equal  to  the 
number  of  wave  lengths  contained  in  the  distance  traveled  per  second 
by  the  train.)  What  effect  has  this  upon  the  pitch?  Had  he  been  going 
from  the  bell  at  this  rate,  how  many  pulses  per  second  would  have  reached 
his  ear  ?   How  would  this  affect  the  pitch  ? 

8.  Explain  the  loud  noise  that  results  from  singing  the  right  pitch 
of  note  into  the  bunghole  of  an  empty  barrel. 

9.  Why  do  the  echoes  which  are  prominent  in  empty  halls  often 
disappear  when  the  hall  is  full  of  people  ? 

CHAPTER  XVII.    1.  What  is  the  wave  length  of  middle  C  when  the 
speed  of  sound  is  1152  ft.  per  second? 

2.  What  is  the  pitch  of  a  note  whose  wave  length  is  5.4  in.,  the  speed 
being  1152  ft.  per  second? 

3.  A  wire  gives  out  the  note  Cwhen  the  tension  on  it  is  4  kg.  What 
tension  will  be  required  to  give  out  the  note  G  ? 

4.  A  wire  50  cm.  long  gives  out  400  vibrations  per  second.     How 
many  vibrations  will  it  give  when  the  length  is  reduced  to  10  cm.  ?   What 
syllable  will  represent  this  note  if  do  represents  the  first  note  ? 

5.  Two  strings,  each  6  ft.  long,  make  256  vibrations  per  second.  If  one 
of  the  strings  is  lengthened  1  in.,  how  many  beats  per  second  will  be  heard? 

6.  If  a  vibrating  string  is  found  to  produce  the  note  C  when  stretched 
by  a  force  of  10  lb.,  what  must  be  the  force  exerted  to  cause  it  to  pro- 
duce (a)  the  note  £?  (b)  the  note  £? 

7.  When  water  is  poured  into  a  deep  bottle,  why  does  the  pitch  of 
the  sound  rise  as  the  bottle  fills  ? 

8.  Show  what  relation  exists  between  the  wave  lengths  of  a  note  and 
the  lengths  of  the  shortest  closed  and  open  pipes  which  will  respond  to 
this  note. 


462 


APPENDIX 


9.  What  must  be  the  length  of  a  closed  organ  pipe  which  produces 
the  note  E  ?    (Take  the  speed  of  sound  as  340  m.  per  second.) 

10.  What  is  the  first  overtone  which  can  be  produced  in  an  open  G 
organ  pipe  ? 

11.  What  is  the  first  overtone  which  can  be  produced  by  a  closed 
C  organ  pipe  ? 

CHAPTER  XVIII.    1.  If  the  opaque  body  in  Fig.  382  is  moved  nearer 
to  the  screen  cf,  how  does  the  penumbra  change  ? 

2.  The  diameter  of  the  moon  is  2000  mi.,  that  of  the  sun  860,000  mi., 
and  the  sun  is  93,000,000  mi.  away.    W^hat  is  the  length  of  the  moon's 
umbra? 

3.  If  the  distance  from  the  center  of  the  earth  to  the  center  of  the 
moon  were  exactly  equal  to  the  length  of  the  moon's  umbra,  over  how 
wide  a  strip  on  the  earth's  surface  would  the  sun  be  totally  eclipsed  at 
any  one  time  ? 

4.  Look  at  the  reflected  image  of  an  electric-light  filament  in  a 
piece  of  red  glass.    Why  are  there  two  images,  one  red  and  one  white  ? 

5.  Show  by  a  diagram  and  explanation  what  is  meant  by  critical  angle. 

6.  The  vertical  diameter  of  the  sun  appears  noticeably  less  than  its 
horizontal  diameter  just  before  rising  and  just  before  setting  because  of 
refraction  due  to  the  earth's  atmosphere.  Explain. 

7.  In  what  direction  must  a  fish  look  in  order 
to  see  the  setting  sun  ?    (See  Fig.  485.) 


FIG.  485.  To  an  eye  under  water  all  exter- 
nal objects  appear  to  lie  within  a  cone  whose 
angle  is  97° 


FIG.  486.   Prism 
glass 


8.  Fig.  486  represents  a  section  of  a  plate  of  prism  glass.  Explain  why 
glass  of  this  sort  is  so  much  more  efficient  than  ordinary  window  glass  in 
illuminating  the  rears  of  dark  stores  on  the  ground  floor  in  narrow  streets. 

9.  In  which  medium,  water  or  air,  does  light  travel  the  faster? 
Give  reasons  for  your  answer. 

10.  Does  a  man  above  the  surface  of  water  appear  to  a  fish  below  it 
farther  from  or  nearer  to  the  surface  than  he  actually  is  ?  Make  an 
explanatory  wave  diagram. 


QUESTIONS  AND  PKOBLEMS 


463 


11.  How  far  from  a  screen  must  a  4-candle-power  light  be  placed  to 
give  the  same  illumination  as  a  16-candle-power  electric  light  3  m.  away? 

12.  If  two  plane  surfaces  placed  1  m.  and  2  m.  respectively  from  a 
given  light  receive  perpendicularly  the  same  quantity  of  light,  how  must 
their  areas  compare?   State  the  law  involved. 

13.  If  two  foot-candles  are  desired  for  reading,  at  what  distance  from 
the  book  must  a  32-candle-power  lamp  be  placed  ? 


CHAPTER  XIX.    1.  An  object  5  cm.  long  is  50  cm.  from  a  concave 
mirror  of  focal  length  30  cm.   Where  is  the  image,  and  what  is  its  size  ? 

2.  Describe  the  image  formed  by  a  concave  lens.  Why  can  it  never 
be  larger  than  the  object? 

3.  What  is  the  focal  length  of  a  lens  if  the  image  of  an  object  10  ft. 
away  is  3  ft.  from  the  lens  ? 

4.  If  the  object  in  Prob- 
lem 3  is  6  in.  long,  how 
long  will  the  image  be  ? 

5.  A  beam  of  sunlight 
falls  on  a  convex  mirror 
through  a  circular  hole  in 

a  sheet  of  cardboard,  as  in     Fm  487>   Determination  of  focal  length  of  a 
Fig.  487.  Prove  that  when  convex  mirror 

the  diameter   of   the    re- 
flected beam  rq  is  twice  the  diameter  of  the  hole  np,  the  distance  mo  from 
the  mirror  to  the  screen  is  equal  to  the  focal  length  oF  of  the  mirror. 

6.  If  a  rose  R  is  pinned  up- 
side down  in  a  brightly  illumi- 
nated box,  a  real  image  may  be 
formed  in  a  glass  of  water  W  by 
a  concave  mirror  C  (Fig.  488). 
Where  must  the  eye  be  placed 
to  see  the  image  ? 

7.  How  far  is  the  rose  from        FlG  48g>  Image  of  object  at  center 
the  mirror  in  the  arrangement  of  curvature 

of  Fig.  488  ? 

8.  A  candle  placed  20  cm.  in  front  of  a  concave  mirror  has  its  image 
formed  50  cm.  in  front  of  the  mirror.    Find  the  radius  of  the  mirror. 

9.  The  parabolic  mirror  used  as  an  objective  in  one  of  the  telescopes 
at  the  Mount  Wilson  observatory  is  100  in.  in  diameter  and  has  a  focal 
length  of  about  50  ft.    What  magnification  is  obtained  when  it  is  used 
with  a  2-inch  eyepiece;  with  a  1-inch  eyepiece?    What  is  gained  by  the 
use  of  a  mirror  of  such  enormous  diameter  ? 


464  APPENDIX 

10.  A  compound  microscope  has  a  tube  length  of  8  in.,  an  objective 
of  focal  length  ^  in.,  and  an  eyepiece  of  focal  length  1  in.    What  is  its 
magnifying  power  ? 

11.  If  the  focal  length  of  the  eye  is  1  in.,  what  is  the  magnifying 
power  of  an  opera  glass  whose  objective  has  a  focal  length  of  4  in.? 

12.  Explain  as  well  as  you  can  how  a  telescope  forms  the  image 
which  you  see  when  you  look  into  it. 

13.  The  magnifying  power  of  a  microscope  is  1000,  the  tube  length 
is  8  in.,  and  the  focal  length  of  the  eyepiece  is  ^  in.    What  is  the  focal 
length  of  the  objective  ? 

CHAPTER  XX.  1.  If  a  soap  film  is  illuminated  with  red,  green,  and 
yellow  strips  of  light,  side  by  side,  how  will  the  distance  between  the 
yellow  fringes  compare  with  that  between  the  red  fringes?  with  that 
between  the  green  fringes?  (See  table  on  page  403.) 

2.  What  will  be  the  apparent  color  of  a  red  body  when  it  is  in  a  room 
to  which  only  green  light  is  admitted  ? 

3.  Will  a  reddish  spot  on  an  oil  film  be  thinner  or  thicker  than  an 
adjacent  bluish  portion? 

4.  Explain  the  ghastly  appearance  of  the  face  of  one  who  stands 
under  the  light  of  a  Cooper-Hewitt  mercury-vapor  arc  lamp. 

5.  Draw  a  figure  to  show  how  a  spectrum  is  formed  by  a  prism, 
and  indicate  the  relative  positions  of  the  red,  the  yellow,  the  green,  and 
the  blue  in  this  spectrum. 

6.  Why  is  a  rainbow  never  seen  during  the  middle  part  of  the  day? 

7.  If  you  look  at  a  broad  sheet  of  white  paper  through  a  prism,  it 
will  appear  red  at  one  edge  and  blue  at  the  other,  but  white  in  the 
middle.   Explain  why  the  middle  appears  uncolored. 

8.  Can  you  see  any  reason  why  the  vibrating  molecules  of  an  incan- 
descent gas  might  be  expected  to  give  out  a  few  definite  wave  lengths, 
while  the  particles  of  an  incandescent  solid  give  out  all  possible  wave 
lengths  ? 

9.  Can  you  see  any  reason  why  it  is  necessary  to  have  the  slit  narrow 
and  the  slit  and  screen  at  conjugate  foci  of  the  lens  in  order  to  show  the 
Fraunhof  er  lines  in  the  experiment  of  §  480  ? 

CHAPTER  XXI.  1.  How  are  ultra-violet  waves  detected?  What 
apparatus  is  used  to  reveal  infra-red  waves? 

2.  Explain  how  the  heat  of  the  sun  warms  the  earth. 

3.  What  is  electric  resonance?   How  may  it  be  demonstrated? 

4.  Describe  the  construction  of  an  X-ray  tube.   Describe  as  well  as 
you  can  the  action  within  it  when  in  use. 


INDEX 


Aberration,  chromatic,  409 

Absolute  temperature,  134 

Absolute  units,  6 

Absorption  of  gases,  102  ff.  ;  of  light 
waves,  414  ;  and  radiation,  419 

Acceleration,  defined,  75 ;  of  gravity, 
77 

Achromatic  lens,  410 

Adhesion,  92  ;  effects  of,  98 

Aeronauts,  height  of  ascent  of,  37 

Air,  weight  of,  26  ;  pressure  of,  27  ; 
compressibility  of,  34 ;  expansi- 
bility of,  34 

Air  pump,  33,  41 

Airplane,  frontispiece  ;  principle  of 
gliding  of,  78-80;  principle  of 
flight  of,  80  ;  Vickers-Vimy,  153  ; 
Liberty  motor  in,  191 ;  Wright,  317 

Airship,  44 

Alternator,  298 

Amalgamation  of  zinc  plate,  272 

Ammeter,  257 

Ampere,  portrait  of,  256 

Ampere,  definition  of,  251, 257 

Ampere  turns,  255 

Amplifier,  431 

Amundsen,  222 

Anode,  248 

Arc  light,  286;  automatic  feed  for, 
287 

Archimedes,  principle  of,  21 ;  por- 
trait of,  22 

Armature,  ring  type,  255, 299  ;  drum 
type,  297,  300,  301,  310 

Atmosphere,  pressure  of,  29  ;  extent 
and  character  of,  36  ;  humidity  of, 
175 

Atoms,  energy  in,  445 

Audion,  429 

Automobile,  195,  198 ;  clutch  and 
transmission,  196;  differential,  197 ; 
carburetor,  198,  199  ;  ignition  sys- 
tem, 198,  199;  anti-glare  "lens," 
362 


Back  E.  M.  F.  in  motors,  303 

Baeyer,  von,  417 

Balance,  7 

Balance  wheel,  141 

Ball  bearings,  145,  146 

Balloon,  kite,  44,  45 ;  dirigible,  44 ; 
helium,  45 

Barometer,  mercury,  30  ;  von  Guer- 
icke's,  31;  the  aneroid,  31;  the  self- 
registering,  32,  38 

Batteries,  primary,  272  ff. ;  storage, 
281,  283 

Battleship,  152 

Bearings,  ball,  145,  146 ;  roller,  146 

Beats,  332,  348 

Becquerel,  441 ;  portrait  of,  446 

Bell,  Alexander  Graham,  316 ;  por- 
trait of,  316 

Bell,  electric,  259 

Bicycle  pedal,  146 

Binocular  vision,  398 

Boiler,  steam,  191 

Boiling  points,  definition  of,  183 ; 
effect  of  pressure  on,  183 

Boyle's  law,  stated,  36;  explained,  51 

British  thermal  unit,  152 

Brittleness,  92 

Brooklyn  Bridge,  143 

Brownian  movements,  52 

Bunsen,  376 

Caisson,  46 

Calories,  152  ;  developed  by  electric 

currents,  289 
Camera,  pinhole,  390 ;  photographic, 

390 
Candle  power,  of  incandescent  lamps, 

285 ;   of  arc  lamps,  286 ;   defined, 

375 

Canner,  steam-pressure,  184 
Capacity,  electric,  240 
Capillarity,  96  ff. 
Capstan,  117 
Carburetor,  198,  199 


466 


466 


INDEX 


Cartesian  diver,  43 

Cathode,  defined,  248 

Cathode  rays,  436 

Cells,  galvanic,  245  ;  primary,  272  ff.; 
local  action  in,  272 ;  theory  of, 
273  ;  Daniell,  275  ;  Weston,  277  ; 
Leclanche",  277 ;  dry,  278  ;  com- 
binations of,  279, 280  j  storage,  281, 
283 

Center  of  gravity,  68 

Centrifugal  force,  84 

Charcoal,  absorption  by,  102 

Charles,  law  of,  136 

Chemical  effects  of  currents,  248 

Cigar  lighter,  platinum-alcohol,  103 

Ciwrnont,  135 

Clouds,  formation  of,  174 

Clutch,  automobile,  196 

Coefficient  of  expansion  of  gases,  136; 
of  liquids,  138  ;  of  solids,  140 

Coefficient  of  friction,  145 

Cohesion,  92;  properties  of  solids 
depending  on,  92 ;  in  liquids,  93  ; 
in  liquid  films,  93 

Coils,  magnetic  properties  of,  252  ff. ; 
currents  induced  in  rotating,  294 

Cold  storage,  202 

Color,  and  wave  length,  402;  of 
bodies,  404  ;  compound,  405 ;  com- 
plementary, 406  ;  of  pigments,  40  7; 
of  thin  films,  408 

Commutator,  298 

Compass,  222.  See  also  Gyrocompass 

Component,  61 ;  magnitude  of,  62 

Concurrent  forces,  60 

Condensation  of  water  vapor,  173 

Condensers,  240 

Conduction,  of  heat,  203 ;  of  electric- 
ity, 227 

Conjugate  foci,  379 

Conservation  of  energy,  155 

Convection,  206  ff . 

Cooling,  of  a  lake,  139;  by  expansion, 
155 ;  and  evaporation,  176 ;  arti- 
ficial, by  solution,  187 

Cooper-Hewitt  lamp,  288 

Coulomb,  251 

Couple,  112 

Crane,  121 

Cream  separator,  85 

Crilley,  46 

Critical  angle,  361,  362 

Crookes,  358, 443  ;  portrait  of,  358 


Curie,  441,  442,  444 ;  portrait  of,  446 
Currents,  wind  and  ocean,  207  ;  elec- 
tric, defined,  245 ;  effects  of  elec- 
tric, 248  ff . ;  magnetic  fields  about, 
252 ;     measurement    of    electric, 
256  ff. ;  induced  electric,  290  ff. 
Curvature,  of  a  liquid  surface,  97 ; 
of  waves,  369  ;  defined,  370 ;  of  a 
mirror,  386  ;  center  of,  463 

Daniell  cell,  275 

Davy  safety  lamp,  205 

Declination,  222 

Densities,  table  of,  8,  9 

Density,  defined,  8;  formula  for,  9; 
of  air,  26 ;  maximum,  of  water, 
138 ;  of  saturated  vapor,  171 ;  of 
electric  charge,  234 

Descartes,  43 

Dew,  formation  of,  174 

Dew  point,  175 

Dewar  flask,  209 

Differential,  automobile,  197 

Diffusion,  of  gases,  50,  52  ;  of  liquids, 
54  ;  of  solids,  55  ;  of  light,  359 

Digester,  184 

Dipping  needle,  223 

Discord,  347 

Dispersion,  403 

Dissociation,  249,  273 

Distillation,  185 

Diving  bell,  45 

Diving  suit,  46 

Doppler  effect,  in  sound,  326 ;  in 
light,  416 

Dry  cell,  278 

Ductility,  92 

Dynamo,  principle  of,  290 ;  rule  for, 
293;  alternating-current,  296;  four- 
pole  direct-current,  300 ;  series- 
wound,  shunt-wound,  and  com- 
pound-wound, 301 ;  defined,  302 

Dyne,  86 

Eccentric,  191 

Echo,  327 

Edison,  356  ;  portrait  of,  316 

Efficiency,  defined,  147  ;  of  simple 
machines,  147 ;  of  water  motors, 
148,  149  ;  of  steam  engines;  193  j 
of  electric  lights,  285  ff. ;  of  trans- 
formers, 312 

Elasticity,  90  ;  limits  of,  91 


INDEX 


467 


Electric  charge,  unit  of,  227  ;  distri- 
bution of,  233 ;  density  of,  234 

Electric  iron,  269 

Electric  motor,  principle  of,  292 ; 
construction  of,  301 ;  defined,  302 

Electricity,  static,  225  ff.  ;  electron 
theory  of,  229,  438  ff. ;  current  of, 
244  ff. 

Electrolysis  of  water,  248 

Electromagnet,  247,  255 

Electromotive  force,  defined,  263 ; 
of  galvanic  cells,  266 ;  induced, 
291 ;  strength  of  induced,  294 ; 
curve  of  alternating,  297;  curve  of 
commutated,  299;  back,  in  motors, 
303 ;  in  secondary  circuit,  307 ;  at 
make  and  break,  308 

Electron  theory,  229,  438  ff . 

Electrophorus,  242 

Electroplating,  249 

Electroscope,  227,  232 

Electrostatic  voltmeter,  239 

Electrotyping,  250 

Energy,  denned,  122  ;  potential  and 
kinetic,  123  ;  transformations  of, 

124,  157,  162,  163  ;  formulas  for, 

125,  126;    conservation  of,    155; 
from  sun,    157 ;    expenditure   of 
electric,  284 ;  stored  in  atoms,  445 

Engine,  steam,  189  ;  steam,  defined, 
191 ;  compound  steam,  193,  298  ; 
gas,  191,  194 

English  equivalent  of  metric  units,  5 

Equilibrant,  60 

Equilibrium,  stable,  69  ;  neutral,  71 ; 
unstable,  71 

Erg,  106 

Ether,  367 

Evaporation,  53 ;  effect  of  tempera- 
ture on,  168  ;  of  solids,  168 ;  effect 
of  air  on,  171,  172  ;  cooling  effect 
of,  176  ;  freezing  by,  178  ;  effect  of 
air  currents  on,  178  ;  effect  of  sur- 
face on,  179  ;  and  boiling,  184 

Expansion,  of  gases,  136  ;  of  liquids, 
138 ;  of  solids,  139  ;  unequal,  of 
metals,  142  ;  cooling  by,  155  ;  on 
solidifying,  165 

Eye,  392  ;  pupil  of,  392  ;  nearsighted, 
393  ;  f  arsighted,  393 

Fahrenheit,  131 
Falling  bodies,  72-78 


Faraday,  251,  290  ;  portrait  of,  290 

Fields,  magnetic,  219 

Films,  contractility  of,  95  ;  color  of, 
408 

Fire  syringe,  155 

Tireless  cooker,  206 

Float  valve,  452  , 

Floating  dry  dock,  448 

Floating  needle,  100 

Flotation,  law  of,  22 

Focal  length,  of  convex  lens,  378; 
of  convex  mirror,  385,  463 

Fog,  formation  of,  174 

Foley,  387 

Foot-candle,  376 

Force,  beneath  liquid,  11 ;  definition 
of,  57  ;  method  of  measuring,  57  ; 
composition  of,  59;  resultant  of, 
59 ;  component  of,  61,  62  ;  centrifu- 
gal, 84  ;  lines  of,  218  ;  fields  of,  219 

Formula  for  lenses  and  mirrors,  388 

Foucault,  358 

Foucault  currents,  309 

Franklin,  236  ;  portrait  of ,  230 ;  kite 
experiment  of,  231 

Fraunhofer  lines,  414 

Freezing  mixtures,  188 

Freezing  points,  table  of,  164  ;  of 
solutions,  187 

Friction,  144  ff. 

Frost,  formation  of,  174 

Fundamentals,  denned,  341 ;  in  pipes, 
349,  350 

Fuse,  electric,  269 

Fusion,  heat  of,  161,  162 

Galileo,    72,    73,  128,  132;   portrait 

of,  72 

Galvani,  245 
Galvanic  cell,  245 
Galvanometer,  256,  257 
Gas  engine,  191,  194 
Gas  heating  coil,  213 
Gas  mask,  103 
Gas  meter,  46  ;  dials  of,  48 
Gay-Lussac,  law  of,  136 
Geissler  tubes,  437 
Gilbert,  225  ;  portrait  of,  222 
Gliding,  principle  of,  78-80 
Governor,  192 
Gram,  of  mass,  4 ;  of  force,  57 ;  of 

force,  variation  of,  58 
Gramophone,  355 


468 


INDEX 


Gravitation,  law  of,  66 

Gravity,  variation  of,  58,  67 ;  center 

of,  68 
Guericke,  Otto  von,  31,  41 ;  portrait 

of,  32 

Gun,  354-mm.,  in  action,  73 
Gyrocom^ss,  83,  223 

Hail,  formation  of,  174 

Hardness,  92 

Harmony,  347 

Hay  scales,  120 

Headlight,  automobile,  400 

Heat,  mechanical  equivalent  of, 
151  ff. ;  unit  of,  152  ;  produced  by 
friction,  153 ;  produced  by  colli- 
sion, 154  ;  produced  by  compres- 
sion, 154  ;  specific,  158 ;  of  fusion, 
161 ;  of  vaporization,  181 ;  trans- 
ference of,  203 

Heating,  by  hot  air,  211 ;  by  hot 
water,  212  ;  by  steam,  213 

Heating  effects  of  electric  currents, 
284,  289 

Helium,  45,  445 

Helmholtz,  345 

Henry,  Joseph,  portrait  of,  246 

Henry's  law,  104 

Hertz,  422,  436  ;  portrait  of,  102 

Heusler  alloys,  216 

Hiero,  21 

Him,  154 

Hooke's  law,  91 

Horse  power,  122 

Humidity,  175 

Huygens,  364,  372  ;  portrait  of,  364 

Hydraulic  elevator,  18 

Hydraulic  press,  17 

Hydraulic  ram,  88,  89 

Hydrogen  thermometer,  132 

Hydrometer,  23 

Hydrostatic  bellows,  447 

Hydrostatic  paradox,  14 

Hygrometry,  173 

Ice,  manufactured,  201 

Ignition,  automobile  system  of,  198, 
199 

Images,  by  convex  lenses,  378  ff. ; 
size  of,  381 ;  virtual,  382 ;  by  con- 
cave lenses,  382 ;  in  plane  mirrors, 
383  ;  in  convex  mirrors,  384,  386 ; 
in  concave  mirrors,  384,  387 


Imp,  bottle,  43 

Incandescent  lighting,  285 

Incidence,  angle  of,  358 

Inclination,  223 

Inclined  plane,  63,  117 

Index  of  refraction,  371 

Induction,  magnetic,  216;  electro- 
static, 228 ;  charging  by,  230 ;  of 
current,  290 

Induction  coil,  308 

Induction  motor,  291 

Inertia,  83 

Insect  on  water,  100 

Insulators,  227 

Intensity,  of  sound,  326 ;  of  illumi- 
nation, 374 

Interference,  of  sound,  333 ;  of  light, 
365 

Ions,  235,  249,  273 

Iron,  electric,  269 

Isoclinic  lines,  457 

Isogonic  lines,  223 

Jackscrew,  118 

Joule,  106, 122, 151  ff.;  portrait  of,  122 

Kelvin,  portrait  of,  134 
Kilogram,  the  standard,  4 
Kilowatt,  122 
Kilowatt  hour,  285 
Kinetic  energy,  123,  126 
Kirchhoff,  415 

Laminated  cores,  310 

Lamps,  incandescent,  285 ;  arc,  286 ; 
Cooper-Hewitt,  288 

Lantern,  projecting,  391 

Leclanch<*  cell,  277 

Lenses,  378  ff . ;  optical  center  of,  378 ; 
principal  axis  of,  378 ;  principal 
focus  of,  378 ;  formula  for,  380 ; 
magnifying  power  of,  395  ;  achro- 
matic, 410 

Lenz's  law,  291 

Level  of  water,  13 

Lever,  110  ff. ;  compound,  120 

Leviathan,  135 

Leyden  jar,  241 

Liberty  motor,  191 

Light,  speed  of,  357 ;  reflection  of, 
358  ;  diffusion  of,  359  ;  refraction 
of,  360;  nature  of,  364;  corpuscular 
theory  of,  364;  wave  theory  of, 


INDEX 


469 


364;  interference  of,  365;  wave 
length  of,  367,  403  ;  intensity  of, 
374;  electromagnetic  theory  of,  436 

Lightning,  236 

Lightning  rods,  236 

Lines,  of  force,  218  ;  isogonic,  223 

Liquids,  densities  of,  9 ;  pressure  in, 
13 ;  transmission  of  pressure  by, 
15;  incompressibility  of,  33;  ex- 
pansion of,  138 

Liter,  3 

Local  action,  272 

Locomotive,  192;  Mallet,  123;  Kocket, 
123 

Loudness  of  sound,  326 

Machines,  general  law  of,  116,  124, 

156  ;  efficiencies  of,  147 
Magdeburg  hemispheres,  33 
Magnet,  natural,  214  ;   laws  of  the, 

215;  poles  of  the,  215;  lifting,  247 
Magnetism,  214  ff. ;  nature  of,  220  ; 

theory  of,  221  ;    terrestrial,  222  ; 

residual,  301 
Magnifying  power,  of  lens,  395  ;  of 

telescope,  396 ;  of  microscope,  397 ; 

of  opera  glass,  398 
Malleability,  92 
Manometric  flames,  343 
Marconi,  423  ;  portrait  of,  316 
Mass,  unit  of,  4;  measurement  of,  6 
Matter,  three  states  of,  55 
Maxwell,  436 ;  portrait  of,  102 
Mechanical  advantage,  109 
Mechanical  equivalent  of  heat,  153  ff. 
Melting  points,  table  of,  164 ;  effect 

of  pressure  on,  166 
Meter,  standard,  3 
Michelson,  357  ;  portrait  of,  358 
Microphone,  315 
Microscope,  397 
Mirrors,  383  ff.;    convex,  384,  386; 

concave,  384, 387 ;  formula  for,  388 
Mixtures,  method  of,  159 
Molecular  constitution  of  matter,  49 
Molecular  forces,  in  solids,  90 ;   in 

liquids,  93 
Molecular  motions,  in"  gases,  49,  50  ; 

in  liquids,  53  ;  in  solids,  55 
Molecular  nature  of  magnetism,  220 
Molecular  velocities,  52, 129 
Moments  of  force,  111 
Momentum  defined,  84 


Morse,  260  ;  portrait  of,  260 

Motion,  uniformly  accelerated,  75 
laws  of,  76  ;  perpetual,  156 

Motor,  Liberty,  191  ;  electric-induc- 
tion, 291  ;  street-car,  302.  See  also 
Electric  motor 

Motor  rule,  293 

Moving  pictures,  386 

Newton,  law  of  gravitation,  66  ;  laws 
of  motion,  83-87  ;  portrait  of,  84  ; 
principle  of  work,  116;  corpuscular 
theory,  364 

Niagara,  157 

Nichols,  E.  F.,  417 

Nodes,  in  pipes,  334  ;  in  strings,  340 

Noise  and  music,  325 

Nonconductors,  of  heat,  205 ;  of  elec- 
tricity, 227 

North  magnetic  pole,  222 

Ocean  currents,  207 

Oersted,  246  ;  portrait  of,  246 

Ohm,  263  ;  portrait  of,  268 

Ohm's  law,  267 

Onnes,  Kamerlingh,  135,  178 

Opera  glass,  398 

Optical  instruments,  890  ff . 

Organ  pipes,  353,  354 

Oscillatory  discharge,  422 

Overtones,  341 ;  in  pipes,  350 

Parabolic  reflector,  400 

Parachute,  44 

Parallel  connections,  270,  280 

Parallelogram  law,  61 

Pascal,  15,  16,  30 

Pendulum,  force  moving,  64 ;  laws 
of,  81 ;  compensated,  141 

Periscope,  400 

Permeability,  217 

Perpetual  motion,  156 

Perrier,  30 

Phonograph,  355 

Photometers,  374,  376 

Pisa,  tower  of,  72 

Pitch,  cause  of,  325 

Pneumatic  inkstand,  33 

Points,  discharging  effect  of,  234 

Polarization,  of  galvanic  cells,  274 ; 
of  light,  374 

Potential,  defined,  237 ;  measure- 
ment of,  239,  265  j  unit  of,  277 


470 


INDEX 


Power,  definition  of,  121 ;  horse,  122  ; 
electric,  284 

Pressure,  in  liquids,  13  ;  defined,  13 ; 
transmission  of,  by  liquids,  15  ;  in 
air,  27  ;  amount  of  atmospheric, 
29 ;  coefficient  of  expansion,  133, 
136;  effect  of,  on  freezing,  166;  of 
saturated  vapor,  1 70  ;  in  primary 
and  secondary,  311 

Projectile,  path  of,  78 

Pulley,  108  ff.;  differential,  119 

Pump,  air,  33,  41 ;  compression,  41 ; 
lift,  42  ;  force,  43 

Quality  of  musical  notes,  342 
Quebec  Bridge,  70 

E-34,  dirigible  airship,  44 

Radiation,  thermal,  208;  invisible, 
417  ff.;  and  temperature,  418 ;  and 
absorption,  419 ;  electrical,  421 

Radioactivity,  441  ff. 

Radiometer,  417 

Radium,  discovery  of,  441 

Rainr  formation  of,  174 

Rainbow,  411 

Ratchet  wheel,  146 

Rayleigh,  portrait  of,  358 

Rays,  infra-red,  417 ;  ultra-violet, 
417 ;  cathode,  437 ;  Rontgen,  439 ; 
Becquerel,  442 ;  a:,  /3,  and  7, 
442  ff. 

Rectifier,  tungar,  314  ;  crystal,  425 

Reflection,  of  sound,  327  ;  of  light, 
358;  angle  of,  358;  total,  361, 
462 

Refraction,  of  light,  360 ;  explana- 
tion of,  368  ;  index  of,  371 

Refrigerator,  163 

Regelation,  167 

Relay,  260 

Resistance,  electric,  defined,  262 ; 
specific,  262;  laws  of,  262;  unit  of, 
263  ;  internal,  268 ;  measurement 
of,  269 

Resistances,  table  of,  262 

Resonance,  acoustical,  328  ff.;  elec- 
trical, 421 

Resonators,  331 

Resultant,  59 

Retentivity,  217 

Retinal  fatigue,  407 

Right-hand  rule,  252,  254 


Rise  of  liquids,  in  exhausted  tubes, 

27  ;  in  capillary  tubes,  97 
Roller  bearings,  146 
Romer,  357 

Rontgen,  439  ;  portrait  of,  446 
Ross,  222 

Rotor,  generator,  257 
Rowland,  155 ;  portrait  of,  358 
Rubens,  408 
Rumford,  151,  374 
Rutherford,  442  ;  portrait  of,  446 

Saturation  of  vapors,  169 ;  magnetic, 
222 

Scales,  musical,  337  ;  diatonic,  338 ; 
even-tempered,  339 

Screw,  118 

Sea  breeze,  207 

Searchlight,  400 

Secondary  cells,  281  ff. 

Self-induction,  307 

Separator,  cream,  85 

Series  connections,  270,  279 

Shadows,  362 

Shunts,  258,  270 

Singing  flame,  348 

Siphon,  explanation  of,  40;  inter- 
mittent, 40 

Siren,  337 

Sleet,  formation  of,  174 

Snow,  formation  of,  174 

Soap  films,  95,  402 

Solar  spectrum,  414,  415 

Sonometers,  339 

Sound,  sources  of,  319;  nature  of, 
319  ;  speed  of,  320  ;  musical,  325  ; 
intensity  of,  326 ;  reflection  of, 
327 

Sound  foci,  328 

Sound  waves,  interference  of,  333 ; 
photographs  of,  346,  387 

Sounder,  260 

Sounding  boards,  331 

Spark,  oscillatory  nature  of  the,  422 ; 
in  vacuum,  436 

Spark  length  and  potential,  240 

Spark  photography,  422 

Speaking  tubes,  326 

Specific  gravity,  9  ;  methods  of  find- 
ing, 22  ff. 

Specific  heat,  defined,  158;  meas- 
ured, 159 

Specific  heats,  table  of,  160 


INDEX 


4T1 


Spectra,   411  ff. ;    continuous,  412 ; 

bright-line,  413  ;  pure,  414 ;  solar, 

414;  X-ray,  447 
Spectrum,  403  ;  invisible  portions  of, 

417 

Spectrum  analysis,  413 
Speed,  of  sound,  320  ;  of  light,  357 ; 

of  light  in  water,  369 ;  of  electric 

waves,  423  ff. 
Spinthariscope,  443 
Starting  box,  304 
Steam  engine,  189  ff. 
Steam  turbine,  199 
Steelyards,  115 
Stereoscope,  398 
Storage  cells,  281,  283 
Strings,  laws  of,  339 
Sublimation,  168 
Submarine,  23,  44 

Sun,  energy  derived  from,  157  ;  spec- 
trum of,  414 
Surface  tension,  95 
Sympathetic  electrical  vibrations,  421 
Sympathetic    vibrations   of    sound, 

346  ff. 

Tank,  British,  190 

Telegraph,  259  ff. ;  wireless,  423  ff. 

Telephone,  316  ff. ;  wireless,  427  ff. 

Telescope,  astronomical,  396;  Yerkes, 
365,  396,  397 

Temperature,  measurement  of,  128  ; 
absolute,  134 ;  low,  134 

Tenacity,  90 

Thermometer,  Galileo's,  128 ;  mer- 
cury, 129  ;  Fahrenheit,  131 ;  gas, 
132-134;  alcohol,  132,  134;  the 
dial,  143 

Thermos  bottle,  209 

Thermoscope,  418 

Thermostat,  142 

Thomson,  438  ;  portrait  of,  440 

Three-color  printing,  408 

Torricelli,  experiment  of,  28 

Tower,  high-tension,  241 

Transformer,  312-314 

Transmission,  of  pressure,  15 ;  elec- 
trical, 312  ;  of  sound,  321 

Transmission,  automobile,  196 

Transmitter,  telephone,  316,  317 

Trowbridge,  418 

Tungar  rectifier,  314 

Turbine,  water,  149 ;  steam,  199 


Units,  of  length,  2 ;  of  area,  2 ;  of 
volume,  2  ;  of  mass,  4  ;  of  time,  5 ; 
three  fundamental,  5  ;  C.  G.  S.,  6  ; 
of  force,  57,  86  ;  of  work,  106  ;  of 
power,  122,  284  ;  of  heat,  152  ;  of 
magnetic  pole,  215  ;  of  magnetic 
field,  219 ;  of  current,  251,  257  ; 
of  resistance,  267 ;  of  potential, 
277  ;  of  light,  375,  376 

Vacuum,  sound  in,  320;  spark  in, 
436 

Vaporization,  heat  of,  181,  182 

Velocity,  of  falling  body,  75;  of 
sound,  320  ;  of  light,  357 

Ventilation,  210,  211 

Vibration,  forced,  331 ;  of  strings, 
339  ;  sympathetic,  346  ff. 

Vibration  numbers,  337 

Vision,  distance  of  most  distinct, 
394  ;  binocular,  398 

Visual  angle,  394 

Volt,  239,  277,  294 

Volta,  245  ;  portrait  of,  240 

Voltmeter,  electrostatic,  239;  com- 
mercial, 265,  266 

Watch,  balance  wheel  of,  141 ;  wind- 
ing mechanism  of,  453 

Water,  density  of,  4  ;  city  supply  of, 
19  ;  maximum  density  of,  138  ;  ex- 
pansion of,  on  freezing,  166 

Water  wheels,  148-150 

Watt,  122,  284 

Watt,  James,  122,  189 ;  portrait  of, 
122 

Watt-hour  meter,  304 

Wave  length,  defined,  322  ;  formula 
for,  323 ;  of  yellow  light,  367 ;  of 
other  lights,  403 

Wave  theory  of  light,  364 

Wave  train,  322,  424,  425 

Waves,  condensational,  323  ;  water, 
324 ;  longitudinal  and  transverse, 
325 ;  light,  are  transverse,  371 ; 
electric,  422  ;  modulated,  427 

Weighing  by  method  of  substitu- 
tion, 6 

Welsbach  mantle,  442 

Weston  cell,  277 

Wet-  and  dry-bulb  hygrometer,  178 

Wheel,  and  axle,  116;  gear,  119; 
worm,  119 ;  water,  148-160 


472  INDEX 

White  light,  nature  of,  403  X-ray  picture  of  human  thorax,  359 

Wind  instruments,  349  X-ray  spectra,  440,  447 

Windlass,  120,  453  X-rays,  439  ff. 

Winds,  207 

Wireless  telegraphy,  423  ff.  Yale  lock,  452 

Wireless  telephony,  427  ff .  Yard,  2 

Work,  defined,  105  ;   units  of,  106  ;  Yerkes  telescope,  365,  396,  397 

principle  of,  116,  125,  156 

Wright,  Orville,  317 ;  portrait  of,  316  Zeiss  binocular,  399 


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